Eirik

Playing the high notes on the clarinet is much like playing the trumpet or the horn; you'll have to hit the exact harmonics. You can hit a A5, E6 or A6 all with the A6 fingering just by using your embouchure. You'll have to bite your way up to the highest notes.

You'll have to train your way up there. Play the notes one by one upwards until you can play them all.
(The Buffet RC Prestige model clarinet I use is also specifically constructed for those high notes.)

BTW, here are the fingerings I use:

High F = High E plus left hand C#/G# key
High F# = High F minus right hand pinky and ring finger
High G = High F# plus right hand index and middle fingers
High G# = High G minus right hand middle finger
High A = High F, but with pinky on the left hand C key
High A# = I don't quite remember it, most fingerings will work if you bite a lot and decide to play an A#
High B = Thumb on hole + octave key, left hand index finger on G# key, left and right hand index and middle fingers on their holes, left hand pinky on the C key, right hand pinky on the C# key
High C = High B minus both hand's middle fingers
Upwards: Press some random keys and press like **** with your teeth. Stop when you start bleeding from your lips :-P
Actually, any fingering will work for the notes above G6. Most keys are added to compensate for flat/sharp tones. Each individual instrument will have its own "best fingerings" and the jungle is yours to explore.