Ironically, when Gotti became Boss, he made sure to strengthen Tommy Gambino's crew by transfering a few soldiers into his regime.

I think Gotti knew Gambino wasn't a threat to his leadership and although he wasn't a big street guy, he was well liked within the family and got some respect because of his father. Not to forget his big money operation in the Garment district. So Gotti was smart enough to keep him around.