Pop:
* P!nk
* Paul McCartney
* Prince
* Pharrell Williams
* Peter Gabriel
* Paloma Faith
* P!nk
* Post Malone
* Dua Lipa (though not strictly "P", the "Dua" part rhymes with "two" and starts with a "P" sound)
Rock/Alternative:
* Pearl Jam
* Peter Gabriel
* Pink Floyd
* Placebo
* PJ Harvey
* The Pixies
* Panic! At The Disco
* Paramore
Country:
* Patsy Cline
* Porter Wagoner
* Patsy Montana
* Porter Robinson
* P!nk (yes, she's also country!)
Soul/R&B:
* Prince
* Patti LaBelle
* Phil Collins
* Percy Sledge
* Peabo Bryson
* Phyllis Hyman
* P!nk
Other:
* Plácido Domingo (Opera)
* Philip Glass (Classical)
* Portishead (Trip-hop)
* PJ Harvey (Experimental Rock)
This list is just a sampling, and there are many other great singers whose names start with P!