Person’s day of birth briefly brought up (3)

I believe the answer is:

bod

'person's' is the definition.
(I've seen this in other clues)

'day of birth briefly brought up' is the wordplay.
'day of birth briefly' becomes 'DOB' (abbreviation for date of birth; 'briefly' asks for a short form).
'brought up' says the letters should be written in reverse (in a down clue, letters go up).
'dob' back-to-front is 'BOD'.

(Another definition for bod that I've seen is " Bloke".)

I've seen this clue in The Times.

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