The 30-year-old signed for the black, green and gold back in July.
But after being drafted in as injury cover, Cook has been unable to make an appearance for Saints.
Alex Mitchell has been a mainstay at scrum-half, starting each of Saints' first five Gallagher Premiership games.
Fiji scrum-half Frank Lomani, a summer signing, has provided back-up for Mitchell in recent weeks and Tom James is on the comeback trail following injury.
Connor Tupai has been playing for Bedford Blues in the Championship but remains an option for Saints if required.
That means former Bath and Bristol player Cook will now move on to pastures new.