If its a mature tree the only pruning it needs is removal of crossing or diseased branches to keep the centre of the tree open, and this is done in the summer. Plums should not be pruned in winter. If its a newly planted young one pruning is different, so let us know.

Don't damage the roots when weeding round it. There is nothing else to do until late winter, when you can dress with sulphate of potash or a general fertilizer. You could give it a nice mulch now though.

Make custard...Mmmm

I was tempted to say pick it, but restrained myself! Custard is good.