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Can I fit the Kalloy expander which says “ 22.2N” to get a bit more height?
No, you can't. That's for 1" threaded headsets/forks. Your bike has a 1 1/8" threadless headset/fork.
You could try some bars with added stack or an even steeper stem.
Is your bike too small/aggressive per chance? Maybe look for an endurance bike instead of this race bike.
Edit: Ah, it's a TT bike. That's going to be quite aggressive with drop bars on it.
The top cap on the Bike say “1.1/8 Ahead Threadless System”
Can I fit the Kalloy expander which says “ 22.2N” to get a bit more height?