Show-off hit six to begin with -- I suspect wanting glory primarily? (13)

I believe the answer is:

exhibitionist

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'show-off' is the definition.
(someone who shows off)

I don't understand the rest of the clue.

(Other definitions for exhibitionist that I've seen before include "Attention-seeker" , "Flasher?" , "Show-off" .)

I've seen this clue in The Telegraph.

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