Did you prune it heavily the year before your lack of fruit began? Plums need only moderate pruning but it must be regularly applied rather than waiting a few years and then severely cutting it back. Additionally, did you have any late freezes or frosts? We experience that difficulty here in the western U.S. and plums are some of the most affected fruiting trees.
Best of luck!
I would only remove any branches which are damaged, together with any which cross. Give a good feed, a couple of handfuls of potash now and in spring. It should soon settle into a fruiting pattern.