In a heart transplant, if the vagus nerve is not re-transplanted, how is the heart rate kept in check?
The heart has its' own pacemaker.
It doesn't need to have a direct nerve connection since it has its' own pacemaker but there is a good chance that the heart rate will be higher at rest.
A pacemaker could be placed to control the heart rate. There has been one study (10 patients) that some nerve reconnections have reoccurred. But that has been debated.