This only ever happens to clarinets where the keys have been either left to rust, or haven't been used in a while. The way around this little problem is to get some key oil and a small needle. Be very careful with this as it is a very tricky operation.

What you need to do is: First of all, fully clean your clarinet as best as you can, even the finger holes. Then you get your needle and very carefully place it in the centre of the key. Now you drop a tiny bit of the oil onto the needle and let it drop into the
key. Take the needle out and start moving the key until it becomes steadily easier to use.

Repeat the whole process again and then move onto the next key. This needs to be done at least once a month to ensure the clarinet is always playing at its best.