How should I replace this ABS p-trap and drain?
You probably won't be able to replace just half of that trap as different manufacturers use different threaded connections at the union. Assuming the "lock ring" you referred to is the union nut (the large nut connecting the two halves of the trap), hand tight is not enough so tightening it carefully with a tool was appropriate. Unfortunately it is common for the nut to crack, causing a leak at the union.

I would cut the black horizontal ABS pipe downstream of the trap and replace the trap with an adjustable P-Trap. This will require a glue joint, but will leave you in a much better position for future repair or replacement when necessary. Use only ABS cement.


Remember, hand tight is not enough. Use adjustable pliers to tighten (but not over tighten) all slip-joint fittings.