diff --git a/babel/src/main/codegen/config.fmpp b/babel/src/main/codegen/config.fmpp
index 001bdf2e1034..8920488dfed5 100644
--- a/babel/src/main/codegen/config.fmpp
+++ b/babel/src/main/codegen/config.fmpp
@@ -582,6 +582,9 @@ data: {
     binaryOperatorsTokens: [
       "< INFIX_CAST: \"::\" >"
       "< NULL_SAFE_EQUAL: \"<=>\" >"
+      "< CONTAINS_OP: \"@>\" >"
+      "< CONTAINED_BY_OP: \"<@\" >"
+      "< OVERLAP_OP: \"&&\" >"
     ]
 
     # Custom identifier token.
@@ -601,6 +604,9 @@ data: {
     extraBinaryExpressions: [
       "InfixCast"
       "NullSafeEqual"
+      "ContainsOp"
+      "ContainedByOp"
+      "OverlapOp"
     ]
 
     # List of files in @includes directory that have parser method
diff --git a/babel/src/main/codegen/includes/parserImpls.ftl b/babel/src/main/codegen/includes/parserImpls.ftl
index 7565303fa008..3f7fa640288b 100644
--- a/babel/src/main/codegen/includes/parserImpls.ftl
+++ b/babel/src/main/codegen/includes/parserImpls.ftl
@@ -221,3 +221,42 @@ void NullSafeEqual(List<Object> list, ExprContext exprContext, Span s) :
     }
     AddExpression2b(list, ExprContext.ACCEPT_SUB_QUERY)
 }
+
+/** Parses the contains operator. */
+void ContainsOp(List<Object> list, ExprContext exprContext, Span s) :
+{
+}
+{
+    <CONTAINS_OP> {
+        checkNonQueryExpression(exprContext);
+        list.add(new SqlParserUtil.ToTreeListItem(
+            SqlLibraryOperators.CONTAINS_OP, getPos()));
+    }
+    AddExpression2b(list, ExprContext.ACCEPT_SUB_QUERY)
+}
+
+/** Parses the contained-by operator. */
+void ContainedByOp(List<Object> list, ExprContext exprContext, Span s) :
+{
+}
+{
+    <CONTAINED_BY_OP> {
+        checkNonQueryExpression(exprContext);
+        list.add(new SqlParserUtil.ToTreeListItem(
+            SqlLibraryOperators.CONTAINED_BY_OP, getPos()));
+    }
+    AddExpression2b(list, ExprContext.ACCEPT_SUB_QUERY)
+}
+
+/** Parses the overlap operator. */
+void OverlapOp(List<Object> list, ExprContext exprContext, Span s) :
+{
+}
+{
+    <OVERLAP_OP> {
+        checkNonQueryExpression(exprContext);
+        list.add(new SqlParserUtil.ToTreeListItem(
+            SqlLibraryOperators.OVERLAP_OP, getPos()));
+    }
+    AddExpression2b(list, ExprContext.ACCEPT_SUB_QUERY)
+}
diff --git a/babel/src/test/java/org/apache/calcite/test/BabelTest.java b/babel/src/test/java/org/apache/calcite/test/BabelTest.java
index aff1aee6604b..97ae6ccbddb1 100644
--- a/babel/src/test/java/org/apache/calcite/test/BabelTest.java
+++ b/babel/src/test/java/org/apache/calcite/test/BabelTest.java
@@ -564,4 +564,50 @@ private void checkSqlResult(String funLibrary, String query, String result) {
         .query("SELECT AGE(timestamp '2023-12-25') FROM (VALUES (1)) t")
         .runs();
   }
+
+  /** Test case for
+   * <a href="https://issues.apache.org/jira/browse/CALCITE-7512">[CALCITE-7512]
+   * Support containment and overlap operators for PostgreSQL</a>. */
+  @Test void testPostgresContainmentAndOverlapOperators() {
+    // Test @> operator: contains
+    checkSqlResult("standard,postgresql",
+        "SELECT ARRAY[1,2,3] @> ARRAY[1,2]",
+        "EXPR$0=true\n");
+    checkSqlResult("standard,postgresql",
+        "SELECT ARRAY[1,2,3] @> ARRAY[4]",
+        "EXPR$0=false\n");
+    checkSqlResult("standard,postgresql",
+        "SELECT ARRAY[1,2,3] @> ARRAY[1,2,3]",
+        "EXPR$0=true\n");
+
+    // Test <@ operator: contained by
+    checkSqlResult("standard,postgresql",
+        "SELECT ARRAY[1,2] <@ ARRAY[1,2,3]",
+        "EXPR$0=true\n");
+    checkSqlResult("standard,postgresql",
+        "SELECT ARRAY[4] <@ ARRAY[1,2,3]",
+        "EXPR$0=false\n");
+    checkSqlResult("standard,postgresql",
+        "SELECT ARRAY[1,2,3] <@ ARRAY[1,2,3]",
+        "EXPR$0=true\n");
+
+    // Test && operator: overlap
+    checkSqlResult("standard,postgresql",
+        "SELECT ARRAY[1,2] && ARRAY[2,3]",
+        "EXPR$0=true\n");
+    checkSqlResult("standard,postgresql",
+        "SELECT ARRAY[1,2] && ARRAY[3,4]",
+        "EXPR$0=false\n");
+    checkSqlResult("standard,postgresql",
+        "SELECT ARRAY[1,2] && ARRAY[1,3]",
+        "EXPR$0=true\n");
+
+    // Test NULL handling
+    checkSqlResult("standard,postgresql",
+        "SELECT ARRAY[1,2] @> NULL",
+        "EXPR$0=null\n");
+    checkSqlResult("standard,postgresql",
+        "SELECT NULL <@ ARRAY[1,2,3]",
+        "EXPR$0=null\n");
+  }
 }
diff --git a/babel/src/test/resources/sql/postgresql.iq b/babel/src/test/resources/sql/postgresql.iq
index af230bd21bd6..56d990c65dcb 100644
--- a/babel/src/test/resources/sql/postgresql.iq
+++ b/babel/src/test/resources/sql/postgresql.iq
@@ -1369,4 +1369,38 @@ X
 ABC
 !ok
 
+# Test PostgreSQL containment and overlap operators
+# @> operator: contains
+select array[1,2,3] @> array[1,2];
+EXPR$0
+true
+!ok
+
+select array[1,2,3] @> array[4];
+EXPR$0
+false
+!ok
+
+# <@ operator: contained by
+select array[1,2] <@ array[1,2,3];
+EXPR$0
+true
+!ok
+
+select array[4] <@ array[1,2,3];
+EXPR$0
+false
+!ok
+
+# && operator: overlap
+select array[1,2] && array[2,3];
+EXPR$0
+true
+!ok
+
+select array[1,2] && array[3,4];
+EXPR$0
+false
+!ok
+
 # End postgresql.iq
diff --git a/core/src/main/java/org/apache/calcite/adapter/enumerable/RexImpTable.java b/core/src/main/java/org/apache/calcite/adapter/enumerable/RexImpTable.java
index 549bddbf724d..628eda8a3203 100644
--- a/core/src/main/java/org/apache/calcite/adapter/enumerable/RexImpTable.java
+++ b/core/src/main/java/org/apache/calcite/adapter/enumerable/RexImpTable.java
@@ -189,6 +189,8 @@
 import static org.apache.calcite.sql.fun.SqlLibraryOperators.CONCAT_WS_MSSQL;
 import static org.apache.calcite.sql.fun.SqlLibraryOperators.CONCAT_WS_POSTGRESQL;
 import static org.apache.calcite.sql.fun.SqlLibraryOperators.CONCAT_WS_SPARK;
+import static org.apache.calcite.sql.fun.SqlLibraryOperators.CONTAINED_BY_OP;
+import static org.apache.calcite.sql.fun.SqlLibraryOperators.CONTAINS_OP;
 import static org.apache.calcite.sql.fun.SqlLibraryOperators.CONTAINS_SUBSTR;
 import static org.apache.calcite.sql.fun.SqlLibraryOperators.CONVERT_ORACLE;
 import static org.apache.calcite.sql.fun.SqlLibraryOperators.COSD;
@@ -263,6 +265,7 @@
 import static org.apache.calcite.sql.fun.SqlLibraryOperators.MONTHNAME;
 import static org.apache.calcite.sql.fun.SqlLibraryOperators.OFFSET;
 import static org.apache.calcite.sql.fun.SqlLibraryOperators.ORDINAL;
+import static org.apache.calcite.sql.fun.SqlLibraryOperators.OVERLAP_OP;
 import static org.apache.calcite.sql.fun.SqlLibraryOperators.PARSE_DATE;
 import static org.apache.calcite.sql.fun.SqlLibraryOperators.PARSE_DATETIME;
 import static org.apache.calcite.sql.fun.SqlLibraryOperators.PARSE_TIME;
@@ -1118,6 +1121,14 @@ void populate2() {
       defineMethod(SUBSTRING_INDEX, BuiltInMethod.SUBSTRING_INDEX.method, NullPolicy.STRICT);
       define(ARRAY_CONCAT, new ArrayConcatImplementor());
       define(SORT_ARRAY, new SortArrayImplementor());
+      // PostgreSQL containment and overlap operators
+      // Uses type dispatch to support multiple operand types (ARRAY, RANGE, JSONB)
+      define(CONTAINS_OP,
+          new ContainmentOpImplementor(BuiltInMethod.ARRAY_CONTAINS_OP.method));
+      define(CONTAINED_BY_OP,
+          new ContainmentOpImplementor(BuiltInMethod.ARRAY_CONTAINED_BY_OP.method));
+      define(OVERLAP_OP,
+          new ContainmentOpImplementor(BuiltInMethod.ARRAY_OVERLAP_OP.method));
       final MethodImplementor isEmptyImplementor =
           new MethodImplementor(BuiltInMethod.IS_EMPTY.method, NullPolicy.STRICT,
               false);
@@ -4689,6 +4700,26 @@ protected MethodCallExpression implementSafe(Method method,
     }
   }
 
+  /** Implementor for PostgreSQL containment and overlap operators.
+   *
+   * <p>Currently supports ARRAY types only.
+   */
+  private static class ContainmentOpImplementor extends AbstractRexCallImplementor {
+
+    private final Method method;
+
+    ContainmentOpImplementor(Method method) {
+      super("containment_op", NullPolicy.NONE, false);
+      this.method = method;
+    }
+
+    @Override Expression implementSafe(final RexToLixTranslator translator,
+        final RexCall call, final List<Expression> argValueList) {
+      return new MethodImplementor(method, nullPolicy, false)
+          .implementSafe(translator, call, argValueList);
+    }
+  }
+
   /** Implementor for the {@code PI} operator. */
   private static class PiImplementor extends AbstractRexCallImplementor {
     PiImplementor() {
diff --git a/core/src/main/java/org/apache/calcite/runtime/SqlFunctions.java b/core/src/main/java/org/apache/calcite/runtime/SqlFunctions.java
index c1ebafe8edd4..2ecf7a71263f 100644
--- a/core/src/main/java/org/apache/calcite/runtime/SqlFunctions.java
+++ b/core/src/main/java/org/apache/calcite/runtime/SqlFunctions.java
@@ -6971,6 +6971,36 @@ public static List arrayUnion(List list1, List list2) {
     return new ArrayList<>(result);
   }
 
+  /** Support for the PostgreSQL {@code @>} (contains) operator. */
+  public static @Nullable Boolean arrayContainsOp(List list1, List list2) {
+    if (list1 == null || list2 == null) {
+      return null;
+    }
+    return new HashSet<>(list1).containsAll(list2);
+  }
+
+  /** Support for the PostgreSQL {@code <@} (contained by) operator. */
+  public static @Nullable Boolean arrayContainedByOp(List list1, List list2) {
+    if (list1 == null || list2 == null) {
+      return null;
+    }
+    return new HashSet<>(list2).containsAll(list1);
+  }
+
+  /** Support for the PostgreSQL {@code &&} (overlap) operator. */
+  public static @Nullable Boolean arrayOverlapOp(List list1, List list2) {
+    if (list1 == null || list2 == null) {
+      return null;
+    }
+    final Set set = new HashSet<>(list1);
+    for (Object item : list2) {
+      if (set.contains(item)) {
+        return true;
+      }
+    }
+    return false;
+  }
+
   /** Transforms a list, applying a function to each element. */
   public static <F, T> List<T> transform(List<? extends F> list,
       Function1<? super F, ? extends T> function) {
diff --git a/core/src/main/java/org/apache/calcite/sql/fun/SqlLibraryOperators.java b/core/src/main/java/org/apache/calcite/sql/fun/SqlLibraryOperators.java
index 2479a92ba247..0294ce811525 100644
--- a/core/src/main/java/org/apache/calcite/sql/fun/SqlLibraryOperators.java
+++ b/core/src/main/java/org/apache/calcite/sql/fun/SqlLibraryOperators.java
@@ -2800,4 +2800,54 @@ private static RelDataType deriveTypeMapFromEntries(SqlOperatorBinding opBinding
               OperandTypes.family(SqlTypeFamily.TIMESTAMP),
               OperandTypes.family(SqlTypeFamily.TIMESTAMP, SqlTypeFamily.TIMESTAMP)),
           SqlFunctionCategory.TIMEDATE);
+
+  /**
+   * The PostgreSQL {@code @>} (contains) operator.
+   *
+   * <p>This operator is polymorphic in PostgreSQL:
+   * <ul>
+   *   <li>ARRAY: checks if left array contains all elements of right array</li>
+   *   <li>RANGE: checks if left range contains the right value/range</li>
+   *   <li>JSONB: checks if left JSON document contains the right JSON document</li>
+   * </ul>
+   *
+   * @see <a href="https://www.postgresql.org/docs/current/functions-array.html">
+   * PostgreSQL Array Functions</a>
+   * @see <a href="https://www.postgresql.org/docs/current/rangetypes.html">
+   * PostgreSQL Range Types</a>
+   * @see <a href="https://www.postgresql.org/docs/current/functions-json.html">
+   * PostgreSQL JSON Functions</a>
+   */
+  @LibraryOperator(libraries = {POSTGRESQL})
+  public static final SqlBinaryOperator CONTAINS_OP =
+      new SqlBinaryOperator("@>", SqlKind.OTHER, 30, true,
+          ReturnTypes.BOOLEAN_NULLABLE, null, OperandTypes.ANY_ANY);
+
+  /**
+   * The PostgreSQL {@code <@} (contained by) operator.
+   *
+   * <p>This operator is polymorphic in PostgreSQL:
+   * <ul>
+   *   <li>ARRAY: checks if left array is contained by right array</li>
+   *   <li>RANGE: checks if left range is contained by right range</li>
+   * </ul>
+   */
+  @LibraryOperator(libraries = {POSTGRESQL})
+  public static final SqlBinaryOperator CONTAINED_BY_OP =
+      new SqlBinaryOperator("<@", SqlKind.OTHER, 30, true,
+          ReturnTypes.BOOLEAN_NULLABLE, null, OperandTypes.ANY_ANY);
+
+  /**
+   * The PostgreSQL {@code &&} (overlap) operator.
+   *
+   * <p>This operator is polymorphic in PostgreSQL:
+   * <ul>
+   *   <li>ARRAY: checks if two arrays have elements in common</li>
+   *   <li>RANGE: checks if two ranges overlap</li>
+   * </ul>
+   */
+  @LibraryOperator(libraries = {POSTGRESQL})
+  public static final SqlBinaryOperator OVERLAP_OP =
+      new SqlBinaryOperator("&&", SqlKind.OTHER, 30, true,
+          ReturnTypes.BOOLEAN_NULLABLE, null, OperandTypes.ANY_ANY);
 }
diff --git a/core/src/main/java/org/apache/calcite/util/BuiltInMethod.java b/core/src/main/java/org/apache/calcite/util/BuiltInMethod.java
index 98b67a02bbf3..d01dbae630ba 100644
--- a/core/src/main/java/org/apache/calcite/util/BuiltInMethod.java
+++ b/core/src/main/java/org/apache/calcite/util/BuiltInMethod.java
@@ -532,6 +532,9 @@ public enum BuiltInMethod {
   IS_JSON_OBJECT(JsonFunctions.class, "isJsonObject", String.class),
   IS_JSON_ARRAY(JsonFunctions.class, "isJsonArray", String.class),
   IS_JSON_SCALAR(JsonFunctions.class, "isJsonScalar", String.class),
+  ARRAY_CONTAINS_OP(SqlFunctions.class, "arrayContainsOp", List.class, List.class),
+  ARRAY_CONTAINED_BY_OP(SqlFunctions.class, "arrayContainedByOp", List.class, List.class),
+  ARRAY_OVERLAP_OP(SqlFunctions.class, "arrayOverlapOp", List.class, List.class),
   ST_GEOM_FROM_EWKT(SpatialTypeFunctions.class, "ST_GeomFromEWKT", String.class),
   UUID_FROM_STRING(UUID.class, "fromString", String.class),
   UUID_TO_STRING(SqlFunctions.class, "uuidToString", UUID.class),