You needn't suffer with unresponsiveness or "clunkiness" when making many large leaps from notes in the clarion register up to notes in the altissimo.
Here's the technique. It's simple:
Finger the clarion note, then ROLL the first finger of your left hand (LH1) away from the tone hole to partially open it. The register change should be smooth and seamless.
If it doesn't work for you, chances are that you're either not exposing enough of the LH1 tone hole, your breath support is insufficient, or you're pinching. (As always, keep a stable embouchure and constant, sufficient, and unchanging breath support.) DO NOT "reach" for the higher note by pinching your embouchure or blowing more or less!
(An observation: Some players are so afraid of horking high notes that they back off on the breath and pinch, like they're walking on eggs. If anything, that's the opposite of what should be done; Keep your breath support steady or maybe increase it a bit, and don't change your embouchure.)
You'll figure out which notes in the clarion go to which notes in the altissimo easiest and with the best intonation. You'll need to experiment. Every setup is different.
In general, "half-holing" LH1 works from any note from the clarion E up to B. You might be able to use this on notes lower than the E even if the tuning suffers, especially if the leap is to a note that won't be held very long
As I wrote, every setup is different, so experiences vary, but I find that leaps from the clarion G upward are the best in tune and the most responsive on my clarinet/mouthpiece/reed combinations. (For some reason I seem to need to move from clarion G to altissimo E the most. I have no idea why this comes up so often.)
Over and out.