The world renowned assassin turns himself in to protect his family,but his last contract didn’t go as planned,now every ruthless assassin hunts down his family.

It reads like this is really about the family. If so, can you single out a family member to make the protagonist?

>>>to protect his family

How is that possible when it seems like turning himself in exacerbates the very problem he was trying to avoid?

>>>now every ruthless assassin hunts down his family.

So.... what must he do about that?? What becomes his objective goal?

If he's a "world renowned assassin"
And he turned himself in
That means his family is as good as dead
because he can't do sh*t from inside

If you mean his goal is to break out and save them...

After failing his last contract, an infamous assassin must break out of prison to save his family from his employers

(throw in some inciting incident too)