care depends on whether your clematis blooms on old wood, new wood, or both. If you have a large-flowered repeat bloomer like ‘Nelly Moser’, ‘The President’, ‘Dr. Ruppel’, or ‘Jackmanii Superba’, it often benefits from gentle deadheading and light tidying now. If you have a heavy spring bloomer that flowers mostly on old wood, you need to be much more careful.
A simple way to sort it out is to think back to when it bloomed most heavily. If it had a big flush in late spring or early summer