I have an old app which was originally built using Xojo in 2012.
I have received an order for this app, but the user is on the latest OS version on M1 chip set.
Are there any possibilities of being able to run this app in the latest version of Mac OS?
No. It would need to be 64 bit and use the Cocoa framework before it would run under Rosetta 2.
macOS 10.14 Mojave is the newest system that can run 32-bit, let alone Carbon apps. Apple never offered Carbon for 64-bit, and by the time of Mojave it had been deprecated for years.
VERY VERY VERY briefly between about 10.5 and 10.6 or so then they yanked it
But it is definitely dead now
Along with 32 bit applications
That must have been when I blinked. 
Yeah they shipped Developer SDKs one year at WWDC then it was gone by the next
Sadly
It would have meant a lot more apps could have transitioned to 64 bit OS X that eventually didnt because they were just to large to move to 64 bit & redo as Cocoa in one fell swoop
Oh well … long ago & far away