I am trying to add the new chase bank app what is the process
I have gone to the App Store and I can't find the chase bank app
On what device did you go to the App Store? There is no Chase app on Macs; you use their website https://www.chase.com/ instead.
On iPhones an iPads if you search for "chase mobile" then you should find the Chase app (although the top result in the search may be another app that has nothing to do with Chase.
Note that this is on an iPhone and iPad with the region set to united States in Settings > General >Language & Region.