CREATE TABLE expire_table (
    timestamp timestamp NOT NULL DEFAULT NOW(),
    name TEXT NOT NULL
);

INSERT INTO expire_table (name) VALUES ('a');
INSERT INTO expire_table (name) VALUES ('b');
INSERT INTO expire_table (name) VALUES ('c');

select * from expire_table;
         timestamp          | name 
----------------------------+------
 2014-09-26 15:33:43.243356 | a
 2014-09-26 15:33:45.222202 | b
 2014-09-26 15:33:47.347131 | c
(3 rows)

CREATE FUNCTION expire_table_delete_old_rows() RETURNS trigger
    LANGUAGE plpgsql
    AS $$
BEGIN
  DELETE FROM expire_table WHERE timestamp < NOW() - INTERVAL '1 minute';
  RETURN NEW;
END;
$$;

CREATE TRIGGER expire_table_delete_old_rows_trigger
    AFTER INSERT ON expire_table
    EXECUTE PROCEDURE expire_table_delete_old_rows();

INSERT INTO expire_table (name) VALUES ('d');

select * from expire_table;
         timestamp          | name 
----------------------------+------
 2014-09-26 15:36:56.132596 | d
(1 row)