DC Cinematic Universe?

I wonder if they'd just pick a new Bruce or if they might do a baton pass to Tim/Dick/Damian?

You could have some time travel shenanigans with The Flash that result in a new Bruce Wayne. I've seen some speculate about this.

You could also go with the "recast and not acknowledge it" tactic, although rumors have said they plan to acknowledge it somehow.

Or you could go with a "Robin becomes Batman" approach. Been done plenty of times in the comics, but will be interesting to see if they think it would work in movies.