My linux cluster has installed ifort compiler now.
But for some purpose, I need pgi compiler in the same computer.
Can they coexist? I'm not familiar with this area, afraid of meeting trouble.
You'll be fine, using multiple compilers (Fortran or any other language) is pretty common, and their default installations shouldn't interfere with each other.
Of course, anytime you're using multiple compilers for a language, you should organize your projects so that you remember which compiler you targeted. At a minimum, make a note in a README or INSTALL file, so that you and other users can easily compile your software in the future.