If you are looking for the official game, you can find it on these platforms: Available on Google Play and sites like Uptodown .
The PSP runs on MIPS architecture (or x86 for PSP Go’s emulation mode), while Temple Run was built for ARM-based mobile devices. Even with custom firmware, you cannot simply drop Android APK files into a PSP. No known emulator can run Temple Run on actual PSP hardware at playable speeds.