Exhaust fan leaking from elbow joint connected to the ceiling
Leaking air, or leaking water?

If leaking air, either replace it if it's degraded, or try duct joint sealant (which stands a somewhat better chance of lasting than duct tape.)



"Leaking" water - a bathroom exhaust vent needs to be heavily insulated all along its length, and should preferably run straight up, then turn and slope gently to the outside, so that water which condenses out of the air can run outside, rather than collecting in the vent and leaking out. Correcting one that's been "leaking" a while may require replacing any corroded sections of vent, improving the routing to more closely match the ideal mentioned above, and wrapping it in insulation. If the joints have been made "the wrong way" (male end inward) you may have to completely re-fit the vent pipe.