To reopen a closed objective:
From the Objectives Overview page, go to a previous quarter (or cycle) where the closed objective lives or otherwise find the closed objective you’d like to reopen
Click on the title of the objective, and you'll be brought to its detail page

Click on ‘Re-open’ objective in the Actions drop-down menu

Once reopened, you’ll be able to check-in and make edits to the objective.
Note: The objective will be reopened for the quarter (or cycle) it was originally assigned for.