Elderly student spoiling gigolos rotten (13)

I believe the answer is:

gerontologist

'elderly student' is the definition.
(I know that gerontologists are students of gerontology)

'spoiling gigolos rotten' is the wordplay.
'spoiling' indicates anagramming the letters.
'gigolos'+'rotten'='gigolosrotten'
'gigolosrotten' with letters rearranged gives 'GERONTOLOGIST'.

(Another definition for gerontologist that I've seen is " He specialises in study of ageing".)

I've seen this clue in The Guardian.

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