How to remove the tailpiece on the p trap that is soldered in place with lead at the face of the wall

Unleaded gas? :)

Small drill, carefully make some holes around the periphery. Then using and awl or similar tool, pick it out. Remove the oakum underneath. Slide tailpiece out.

Hmmmm... put a new one back in?

Look at my question earlier on this forum about joining 4" PVC to cast iron hub... guessing you have a cast iron hub that you wish to put new tailpiece into. Same principle, just substitute 1 1/2" pipe instead. Speedball set me straight on how that's done. There's several different methods explained in that post.

Good luck!