I keep having a notification exclamation icon at the Drivers & Staff menu option. The icon also shows on my Chief Designer tile on the Staff tab. I renewed his contract 3 races ago so he still has 47 races on this contract. Therefore I don't think a notification is necessary :-) I renewed his contract 1 race before it ended, if that helps.
On top of that I was caught by surprise when my TD ran out of contract _without_ notification earlier. I didn't have any tokens at that time, so I had to do one race with a 1 star TD as a consequence.