I am in zone 9b and have an apple tree (multi-varietal) that has been growing in all directions because of lack of proper pruning. I am interested in knowing when I can prune this tree in my zone and how best to prune it. As you see from the picture some of the unwanted stems are pretty thick and I want to know is cutting them off is a good idea in addition to where else I can prune to get the tree back in shape.
First get rid of all those plastic 'ties'...now before the limbs have to have them for support. Cut all vertical shoots. All shoots that are not the direction you want with this espalier. It is OK for that amount of room. I'd get some horizontal wires, eyelet screws and something to keep 4 to 6 inches from your fence, permanently installed to train your limbs into the espalier. Nicely installed with correct hardware and a good thick wire. Those ties make for very weak branches and here we don't even have the weight of fruit.
Make sure you clean your pruners (bypass not anvil) with alcohol before touching your apple espalier.
That limb on our left in the picture needs to be pulled back, gently, consistently to get in line with the rest of the horizontals. Don't hurry or fret it is easy to train, just a bit of patience. All ties and all constricting wires need constant vigilance and commitment to short term and/or change.
Check that trunk where it meets the soil. Make dang sure NO trunk is buried otherwise you can kiss this wonderful apple espalier goodbye. Pull the soil way back...this next fall we should discuss how to raise this tree so that trunk is not buried or so low it is in danger of girdling rot.
One thing to bear in mind with family trees is that the different varieties grafted on may grow with widely different growth habits. In the worst case, one vigorous variety may produce so much foliage causing shade and draw so much nutrient from the main trunk that other weaker shoots will diminish rapidly. Weight of fruit and branch volume may cause the tree to become lop-sided over time until the strong takes over completely.
Consider summer pruning the shoots and fruit thinning of the most vigorous varieties to allow light to penetrate to the weaker shoots and keep the tree balanced.