If you mean the michaelmas daisy type of aster you can cut them down to the ground if you want to. They disappear in the winter anyway.

I leave the stems on over winter as they help protect next yrs new growth from the worst of the weather. they also provide shelter for useful insects like ladybirds too.

but if you like the garden tidy then you can cut them down to ground level as and when you fancy tackling them.

If you are talking about the annual bedding type then pull them up and compost or bin which ever you prefer.

Thanks. They are the shrubby perennial type. Looks as though I can neglect them and they will come again next year. Thanks both for your advice.
Miriam.

hello Miriam,
I was treated to the sight of a small flock of goldfinches feeding on the seed heads of mine in the middle of last winter, so they are definitely worth leaving until spring. And as seaburngirl says, they provide a winter home for a myriad of small creatures.