diff --git a/.unreleased/fix_6339 b/.unreleased/fix_6339
new file mode 100644
index 00000000000..b4f4290cb34
--- /dev/null
+++ b/.unreleased/fix_6339
@@ -0,0 +1,2 @@
+Fixes: #6339 Fix tablespace with constraints
+Thanks: @lyp-bobi for reporting the issue
diff --git a/sql/chunk_constraint.sql b/sql/chunk_constraint.sql
index 0b0a815870d..1d205b236fe 100644
--- a/sql/chunk_constraint.sql
+++ b/sql/chunk_constraint.sql
@@ -40,10 +40,6 @@ BEGIN
 
           def := pg_get_constraintdef(constraint_oid);
 
-          IF indx_tablespace IS NOT NULL THEN
-            def := format('%s USING INDEX TABLESPACE %I', def, indx_tablespace);
-          END IF;
-
         ELSIF constraint_type = 't' THEN
           -- constraint triggers are copied separately with normal triggers
           def := NULL;
@@ -63,6 +59,18 @@ BEGIN
             $$ ALTER TABLE %I.%I ADD CONSTRAINT %I %s $$,
             chunk_row.schema_name, chunk_row.table_name, chunk_constraint_row.constraint_name, def
         );
+
+        -- if constraint (primary or unique) needs a tablespace then add it
+        -- via a separate ALTER INDEX SET TABLESPACE command. We cannot append it
+        -- to the "def" string above since it leads to a SYNTAX error when
+        -- "DEFERRABLE" or "INITIALLY DEFERRED" are used in the constraint
+        IF indx_tablespace IS NOT NULL THEN
+            EXECUTE pg_catalog.format(
+                $$ ALTER INDEX %I.%I SET TABLESPACE %I $$,
+                chunk_row.schema_name, chunk_constraint_row.constraint_name, indx_tablespace
+            );
+        END IF;
+
     END IF;
 END
 $BODY$ SET search_path TO pg_catalog, pg_temp;
diff --git a/sql/updates/reverse-dev.sql b/sql/updates/reverse-dev.sql
index 7f33372ef99..123d39f252c 100644
--- a/sql/updates/reverse-dev.sql
+++ b/sql/updates/reverse-dev.sql
@@ -333,3 +333,72 @@ BEGIN
   END LOOP;
 END;
 $$ LANGUAGE PLPGSQL;
+
+DROP FUNCTION _timescaledb_functions.chunk_constraint_add_table_constraint(
+    chunk_constraint_row  _timescaledb_catalog.chunk_constraint
+);
+
+CREATE FUNCTION _timescaledb_functions.chunk_constraint_add_table_constraint(
+    chunk_constraint_row  _timescaledb_catalog.chunk_constraint
+)
+    RETURNS VOID LANGUAGE PLPGSQL AS
+$BODY$
+DECLARE
+    chunk_row _timescaledb_catalog.chunk;
+    hypertable_row _timescaledb_catalog.hypertable;
+    constraint_oid OID;
+    constraint_type CHAR;
+    check_sql TEXT;
+    def TEXT;
+    indx_tablespace NAME;
+    tablespace_def TEXT;
+BEGIN
+    SELECT * INTO STRICT chunk_row FROM _timescaledb_catalog.chunk c WHERE c.id = chunk_constraint_row.chunk_id;
+    SELECT * INTO STRICT hypertable_row FROM _timescaledb_catalog.hypertable h WHERE h.id = chunk_row.hypertable_id;
+
+    IF chunk_constraint_row.dimension_slice_id IS NOT NULL THEN
+	    RAISE 'cannot create dimension constraint %', chunk_constraint_row;
+    ELSIF chunk_constraint_row.hypertable_constraint_name IS NOT NULL THEN
+
+        SELECT oid, contype INTO STRICT constraint_oid, constraint_type FROM pg_constraint
+        WHERE conname=chunk_constraint_row.hypertable_constraint_name AND
+              conrelid = format('%I.%I', hypertable_row.schema_name, hypertable_row.table_name)::regclass::oid;
+
+        IF constraint_type IN ('p','u') THEN
+          -- since primary keys and unique constraints are backed by an index
+          -- they might have an index tablespace assigned
+          -- the tablspace is not part of the constraint definition so
+          -- we have to append it explicitly to preserve it
+          SELECT T.spcname INTO indx_tablespace
+          FROM pg_constraint C, pg_class I, pg_tablespace T
+          WHERE C.oid = constraint_oid AND C.contype IN ('p', 'u') AND I.oid = C.conindid AND I.reltablespace = T.oid;
+
+          def := pg_get_constraintdef(constraint_oid);
+
+          IF indx_tablespace IS NOT NULL THEN
+            def := format('%s USING INDEX TABLESPACE %I', def, indx_tablespace);
+          END IF;
+
+        ELSIF constraint_type = 't' THEN
+          -- constraint triggers are copied separately with normal triggers
+          def := NULL;
+        ELSE
+          def := pg_get_constraintdef(constraint_oid);
+        END IF;
+
+    ELSE
+        RAISE 'unknown constraint type';
+    END IF;
+
+    IF def IS NOT NULL THEN
+        -- to allow for custom types with operators outside of pg_catalog
+        -- we set search_path to @extschema@
+        SET LOCAL search_path TO @extschema@, pg_temp;
+        EXECUTE pg_catalog.format(
+            $$ ALTER TABLE %I.%I ADD CONSTRAINT %I %s $$,
+            chunk_row.schema_name, chunk_row.table_name, chunk_constraint_row.constraint_name, def
+        );
+
+    END IF;
+END
+$BODY$ SET search_path TO pg_catalog, pg_temp;
diff --git a/test/expected/constraint.out b/test/expected/constraint.out
index ec7e953f7aa..b22baab9360 100644
--- a/test/expected/constraint.out
+++ b/test/expected/constraint.out
@@ -812,7 +812,7 @@ CREATE TABLE tbl (
 fk_id int,
 id int,
 time timestamp,
-CONSTRAINT pk PRIMARY KEY (time, id) USING INDEX TABLESPACE tablespace1);
+CONSTRAINT pk PRIMARY KEY (time, id) USING INDEX TABLESPACE tablespace1 DEFERRABLE INITIALLY DEFERRED);
 SELECT create_hypertable('tbl', 'time');
 WARNING:  column type "timestamp without time zone" used for "time" does not follow best practices
  create_hypertable 
diff --git a/test/sql/constraint.sql b/test/sql/constraint.sql
index 1603422f0b2..9861b798e9c 100644
--- a/test/sql/constraint.sql
+++ b/test/sql/constraint.sql
@@ -612,7 +612,7 @@ CREATE TABLE tbl (
 fk_id int,
 id int,
 time timestamp,
-CONSTRAINT pk PRIMARY KEY (time, id) USING INDEX TABLESPACE tablespace1);
+CONSTRAINT pk PRIMARY KEY (time, id) USING INDEX TABLESPACE tablespace1 DEFERRABLE INITIALLY DEFERRED);
 
 SELECT create_hypertable('tbl', 'time');