If it's the hot and not the cold, then you pull off the supply to the faucet and check to see if water flows at that point.
Since the cold seems good, it's not something common to both like an aerator.
Sometimes the steel pipes leading to the brass shutoffs corrode down to nothing.
Replacing the short section of pipe, replacing the stop and supply may be all that's needed.
Not an easy job, the last one I did I had sore muscles for a day.
It was not easy to get too, and had been there a very long time.