I installed a new sink that is one inch deeper than my old one. I can pull down the pipe and barely screw my p trap in, but now it leaks. I went looking for an extension piece, but the threads weren't right. I;m at my wits end!

Try installing the trap backwards.

Cut the Tail piece 1" shorter... All threads should be the same... Post a pic so we see what you are doing... Back to you... Milo

Milos solution sounds like it would work if you have the space to cut it back, Or you could do what I did when I installed a deep lavatory for my neighbor that was too low to hook up to the wall stubout, I built a trap out of PVC that raised enough to make the connection. Good luck, Tom