A phrase or expression for: Work on task 2 is dependant on task 1 finishing
How about conditioned, derived from condition? From Cambridge:
condition: an arrangement that must exist before something else can happen
Your example:
The completion of task 2 is conditioned on the completion of task 1.
A related possibility is the mathematical term necessary condition.
Your example:
The completion of task 1 is a necessary condition for the completion of task 2.
That is, task 2 cannot be completed unless and until the necessary condition -- the completion of task 1 -- has been met first.
Task 2 is contingent on the completion of task 1.