No, there is no time limit. In fact there is no requirement at all to buy a gun once you have a shotgun licence.
You could, for example, have a shotgun licence just so you can borrow a gun from a friend for up to 72 hours.
This is much more flexible than borrowing a gun and using it in the owner’s presence, which you can do without a shotgun licence.
One way of getting some shooting if you’re hard up is to beat regularly on a shoot during the winter and enjoy the beaters’ day, which most shoots now offer to their regulars.
There’s bound to be someone who would lend you a gun for that or maybe for a spot of pigeon shooting.