What to do with our plum tree?
 

Hello

We have a plum now three years old. To my wife's delight, last year it
produced 3 plums.

This year, it's producing NONE. However it has produced dozens and
dozens of new leafy branches ... it's turned into a huge bush.

I get the feeling that I ought to be pruning it and shaping it now,
while this plethora is still flourishing: any advice?

TIA
John