The Redgrave Theatre is 5-8 minutes walk from Clifton Village and 12-15 minutes walk from Whiteladies Road. It is probably easier to park on the street close to the theatre than it is to park in the Village. There is no official car park nearby but on-street parking is available after 5pm. College Fields opposite the Redgrave Theatre is probably the best option for parking.
If you are coming from outside the area you are advised to arrive early, go for a drink or a meal in Clifton Village which is 5-8 minutes walk away.