Blue tit nesting habits

I have recently moved home and thankfully the previous owners have been feeding the birds. There are a couple of nesting boxes and one had an old nest in it. Today I noticed, a I think a blue tit inspecting outside before going in. I have read on this site they do this and it may  use it over the winter. I haven't removed the old nest yet. I didn’t think birds reused nests. Should I leave it there or remove at some point.