Manager change when close to promotion

Few months ago during 1:1 with my manager, I was told that if I successfully delivered project on time they'd initiate my promotion request with higher ups. Fast forward two months, completed the project on time. Found out that I'd reporting to a new manager henceforth. I am hoping that the new manager will be scheduling a meeting quite soon. When it happens, I'd like to bring up my promotion topic. How exactly should I bring up this topic? Would appreciate any advise from others who have been in similar situation.