Technically you can keep your clarinet assembled, but ideally, it is best to only do this for short periods of time. Never leave your clarinet just lying around or balanced anywhere precariously, always use a clarinet stand to keep it safe.
If you are leaving your clarinet on its own for long periods of time, make sure that you clean it out and disassemble it and put it back in its case. This means that it makes sure that the clarinet stays safe, dry and in good working order.