"To find a successor" means to identify and select someone who can take over a certain position or role once the current person leaves or retires. Full definition
After all, if you don't eventually find your successor, you're going to be stuck in that job forever anyway. (inc.com)
That would tie the university's hands for a time if the program was underperforming, and possibly even limit options in finding a successor. (sbnation.com)
The committee will be responsible for finding a successor for Callahan. (nreionline.com)