Cryptically praise British rock (3)

I believe the answer is:

gib

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'rock' is the definition.
(both are nicknames for Gibraltar)

'cryptically praise british' is the wordplay.
I cannot quite see how this works, but
'british' could be 'b' (abbreviation e.g. in 'BBC') and 'b' is found within the answer.
The remaining letters 'gi' is a valid word which might be clued in a way I don't understand.
This may be the basis of clue (or it may be nonsense).

Can you help me to learn more?

(Another definition for gib that I've seen is " The Rock".)

I've seen this clue in The Independent.

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