Hi there.

If it's only 4 years old, and was properly pruned before you bought it, it shouldn't need any pruning at this early stage.

Don't worry about it not fruiting - plums generally begin to fruit when they're about 5 years old.

I would only do a cautious thinning for structure, removing crossing branches and narrow crotches. I would try not to remove more than 20% of the foliage (or future foliage) in the process, since that could delay fruiting more. As for timing, people from the UK could advise you better than I could, since there is a disease there that would attack the tree if you pruned it at the proper time for Phoenix, AZ!

It;s a little late to prune anyway, you risk silverleaf infection if you do it now - May is a good time, and midsummer for established, more mature trees.

Ah! Silverleaf is what I was trying to think of! Glad we don't have that here in the U.S.!