Rock with primate half visible? (3)

I believe the answer is:

gib

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

'primate half visible?' is the wordplay.
'primate' becomes 'gibbon' (gibbon is a kind of primate).
'half visible?' suggests halving the letters.
'gibbon' halved is 'GIB'.

'with' acts as a link.

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

I've seen this clue in The Times.

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