IMDb currently lists writing duties being handled by Andre Nemec and Josh Applebaum, who previously wrote Mission: Impossible – Ghost Protocol as well as the most recent pair of Teenage Mutant Ninja Turtles movies.
This is obviously an entirely fresh take as the new directors haven’t seen any script previously.
It seems that the script for Beverly Hills Cop 4 has been a tough nut to crack for years, as that was the issue back in 2015 when the project was being handled by Brett Ratner.