I kind of beat the drum a bit that any new to you used boat needs every bit of maintenance done by you before running your boat. The assumption must be that the maintenance was neglected. That means pulling the drive, draining it, splitting the halves, inspecting everything, replacing the impeller and or water pump housing, inspecting driveshaft, u-joints, gimbal bearing, bellows, shine a flashlight on the couplers and so on. Look at the maintenance requirements and perform all the relevant tasks.
Taking it out on the water and hearing a problem is just an expected result of not doing the above.