The roads adjacent to the Royal Spa Centre have plenty of pay-and-display on-street parking spaces which are unrestricted after 6pm.
The nearest, large car park is the multi-story at St Peter's on Augusta Place (use the postcode CV32 5EL). It costs £3.80 to park here for up to 3 hours, and it's a 10-12 minute walk to the theatre at buggy pace.
The closest car park to the venue is Rosefeild Street CV32 4HN, just a few feet away however this is a very small car park with only 47 spaces, 2 designated disabled bays, 1 motorcycle bay and will usually be full. This car park only accepts bank card and Ring Go payments (see here for more details: https://www.warwickdc.gov.uk/ringgo)
Please allow plenty of time to make sure you can find a place to park!
Visit https://www.warwickdc.gov.uk/info/20546/leamington_car_parks to see all the available parking options near the Royal Spa Centre.