I believe I need a new tailpipe connecting to the muffler in order to stop a leak.
The metal components of the exhaust system tolerate many stresses along with changes in weather and constant moisture. These events allow rust to build along the pipes and eventually may rust through. Some of the rusty sections can be cut out and replaced with new piping. For this repair, I would consult a collision or muffler shop. If you need a diagnostic, you could also get a certified technician from YourMechanic to come out and inspect the leak before having taking your next steps.