I don’t have as much experience as some people here with espalier, but I’ve been growing up 7 espalier apples on my back fence for 6 years now. Also, a lot of this stuff is not able to be completely right or wrong and people follow different philosophies about shaping and pruning principles for espalier.
My feeling on your picture is that I would cut the big branch cluster on the left as you have drawn in purple. Yes, the general idea is to cut with three buds left over on the stub, but I think if the side stub is more than 1/2 the diameter of the main branch, it could stand to be removed entirely. This is from my interpretation of a guideline @alan has espoused elsewhere and I think it makes sense. Otherwise your whole structural layout will eventually be compromised. In your case that cluster is almost as big as the main branch and not going to get any smaller. Especially if you cut it in dormancy, there is some chance your main branch will pop some latent buds into shoots which could eventually turn into spurs or new stub branches. Though there is also some chance that won’t happen and you will end up with a bare spot. I guess I’m more willing than some to sacrifice a few potential apples for the next season in return for keeping the long term shape on track.
I could also see cutting the part on your right purple line, but I could also see leaving it and cutting the shoots to three buds.
Thanks for the comments @HollyGates. I think you are right about that branch on the left - it is actually thicker than the main horizontal branch now and I do worry about comprising the tiered layout.
I’ve found a photo of the same part of the tree which I took last year and this is how it looked after pruning in February 2019
It’s rather startling to see how much it has grown in one year! Incredible how the little branch to the right of the main trunk has grown in one year too!
It makes me realise how correct the advice that winter pruning encourages growth is! I’m definitely going to pinch back more this summer. Is that what you have done on your trees?
Our house was built in 1723, hence the glorious stone walls - the espaliered trees are against one of the outbuildings which provide a lovely backdrop for my traditional French vegetable garden.
@thepodpiperdo you have any experience with tip bearing varieties? I’ve been cutting all of mine back but have recently wondered if they are not the spurring kind.
How did your 4 year old espalier fruit tree respond to this 5/15 pruning? I got no flowers yet on my pear and few on my apple. I am pruning it today (zone 6a) I could really use some guidance.
I could really learn to do what ever you did!!! I am pruning off water sprouts right now, but think I need to do more. I got zero flowers on my pear this year.
