diff --git a/src/bin/psql/tab-complete.c b/src/bin/psql/tab-complete.c
new file mode 100644
index a62ffe6..85f7a1c
*** a/src/bin/psql/tab-complete.c
--- b/src/bin/psql/tab-complete.c
*************** static const SchemaQuery Query_for_list_
*** 820,825 ****
--- 820,832 ----
  "  WHERE (%d = pg_catalog.length('%s'))"\
  "    AND pg_catalog.quote_ident(name)='%s'"

+ /* the silly-looking length condition is just to eat up the current word */
+ #define Query_for_list_of_available_extension_versions_with_TO \
+ " SELECT 'TO ' || pg_catalog.quote_ident(version) "\
+ "   FROM pg_catalog.pg_available_extension_versions "\
+ "  WHERE (%d = pg_catalog.length('%s'))"\
+ "    AND pg_catalog.quote_ident(name)='%s'"
+ 
  #define Query_for_list_of_prepared_statements \
  " SELECT pg_catalog.quote_ident(name) "\
  "   FROM pg_catalog.pg_prepared_statements "\
*************** psql_completion(const char *text, int st
*** 1414,1419 ****
--- 1421,1440 ----
  	else if (Matches3("ALTER", "EXTENSION", MatchAny))
  		COMPLETE_WITH_LIST4("ADD", "DROP", "UPDATE", "SET SCHEMA");

+ 	/* ALTER EXTENSION <name> UPDATE */
+ 	else if (Matches4("ALTER", "EXTENSION", MatchAny, "UPDATE"))
+ 	{
+ 		completion_info_charp = prev2_wd;
+ 		COMPLETE_WITH_QUERY(Query_for_list_of_available_extension_versions_with_TO);
+ 	}
+ 
+ 	/* ALTER EXTENSION <name> UPDATE TO*/
+ 	else if (Matches5("ALTER", "EXTENSION", MatchAny, "UPDATE", "TO"))
+ 	{
+ 		completion_info_charp = prev3_wd;
+ 		COMPLETE_WITH_QUERY(Query_for_list_of_available_extension_versions);
+ 	}
+ 
  	/* ALTER FOREIGN */
  	else if (Matches2("ALTER", "FOREIGN"))
  		COMPLETE_WITH_LIST2("DATA WRAPPER", "TABLE");