Will my Box hedge be ok?

Hello!

My other half wanted to get rid of a box hedge that I planted about 5-6 years ago. We have a very steep back garden and it's above our patio which can feel a little oppressive at times - it was originally planted to stop the kids falling off the wall when they were young!! By way of a compromise, I cut it back hard yesterday (April 5th) taking about a 3rd off the top and trimming new growth off both sides. Do you think it's will survive?