Hi Jodene and welcome to GoY I think it highly unlikely that you could turn this into an espalier. It isn't the nature of the shrub. However, I'm sure others will chip in with their comments.

Highly unlikely, and actually not a good idea - this appears to be Chaenomeles japonica rather than Cydonia (true quince) and although it does produce edible fruits which can be made into quince jelly, its actually grown for its red flowers, which arrive on bare wood just before the leaves. Not sure the one in your picture has been pruned this year, looks a bit unruly, but the usual time to prune is just after flowering - pruning it hard now means you won't get many flowers, if any, in spring. You can either prune it when its dormant (after the leaves have gone) now and sacrifice any blooms you might have got, or wait until its finished flowering in spring.

Since it is Chaenomeles, a species that I am familiar with, I might be able to offer advice from my experience with bonsai. I would need to see the structure of the bush with its leaves off, though. I'll admit that I am assuming that you mean the bush in the foreground, which looks hopeful, instead of the small tree in the background, which...doesn't, so much.

As it seems to be Chaenomeles (Japanese Quince) I would have said it would have made a good fan subject rather than espalier but you would have needed to have begun with a younger plant. I wouldn't consider trying to adapt this one.

Definitely not a formal espalier, true.