I am using Office XP on my 2010 MacBook Air. Will this run on new MacBook air 2023"

No Apple Silicon Macs (M1 - M3) support Boot Camp (which no longer supports Win XP anyway), and even a Virtual Machine (e.g. Parallels, VMware) cannot run Intel compiled Windows operating system guests on an Apple Silicon Mac.

The free UTM virtual machine can run an Intel compiled version of Windows XP on Apple Silicon, but expect it to be measurably slower as it is done with emulation.

If you plan to use UTM, consider purchasing the new Air with 24GB RAM. As far as I know, the new model MacBook Air still have no internal fan (the MacBook Pro do) and may run warm using UTM.

That is a really old Windows program, and the Mac version (Office X) dates from 2001. I’m pretty sure that it (if you mean Office X) won’t run on a new Mac.

Microsoft makes current versions of 365/Office for Apple Silicon Macs.