The court will write to the DVLA to tell them they have reduced your ban if successful. There is no reason why you couldn't apply the same day, although it would be wise to include a covering note explaining the circumstances in case your application is processed before the notification from the court.
After that you will need to have the HRO medical which can take a couple of months, so you won't quite be reducing your ban by a whole year, as you can start the HRO process three months before your original ban ends, meaning (in theory) your licence should be ready at the end of the three years.