You can't run an HP-compiled binary on Linux, but you might be able to go the other way (run a Linux-compiled binary on HP). HP has been working on binary compatibility for Linux (and so has IBM), but mainly with HP running on Itanium chips. I don't know the current status, and I've never tried it.
If you have the source code, you might be able to just recompile - assuming all your APIs are POSIX standard.