I believe you keep all the scouting effort by the previous coach, but you won't receive any of the recruiting effort.
If there had been recruiting effort put into a recruit, you should see a line adjustment called New Coach adjustment on the recruiting History tab.
Be warned, that I've seen what appears to be a bug twice in the past few months. The recruiting visits are listed that you've used some of the trips, but you are receiving none of the credit for them. Customer Service can reset which allows you to then use the visits.