Sorry its not clear what you mean. Are you wanting to make your arch higher or to stop it getting any higher?

Do you mean that you want to cut the privet into an arch shape once its high enough? If so, the best way to do that is to cut it into an arch shape from the outset. If you wait till it's high, you'll have to cut right into the hedge to get the shape, and it will look dreadful for at least a couple of years (and may never fully clothe itself at all).

If you mean something else entirely, please supply more information and someone will be happy to help.

Hi, welcome to GoY, you really need a plant either side of the arch, and it will take a few years to get to a height suitable for training over the arch, to start with, you will need to clip it back 2 or 3 times a year, so that it doesn't get tall and leggy, with nothing at the bottom, build the height up gradually, until the privet is higher than your arch, when this is achieved, allow the shoots that are facing towards the arch to extend slightly over it, then cut them back to encourage more shoots to make what will now be the top of your arch more bushy, you should cut back any shoots that start to grow upwards from the top of the arch, eventually the 2 plants will meet in the middle, { or thereabouts }, then trim normally, remembering not to cut off the original branches that you allowed to go over the arch, or all your work will come to nothing, as I say it will take several years to achieve the desired effect, I think you would be much better off using an evergreen climber, I don't like privet at the best of times, and this needs a lot of patience, Derek.

I think privet gets a bad press actually. Its nowhere near as bad as leylandii even though its just as greedy. We inherited a long hedge of it and it actually looks quite neat, though it does need trimming oftener than other hedges, which would be a drawback for a mature arch.