Cook had advanced qualification (9)

I believe the answer is:

doctorate

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'advanced qualification' is the definition.
'doctorate' can be an answer for 'qualification' (I've seen this before). I'm not sure about the 'advanced' bit.

'cook had' is the wordplay.
'cook' becomes 'doctor' (I've seen this before).
'had' becomes 'ate' (e.g. I had an ice cream).
'doctor'+'ate'='DOCTORATE'

Can you help me to learn more?

(Other definitions for doctorate that I've seen before include "PhD or D.Phil" , "Highest academic degree" , "Higher degree" , "Academic qualification" , "Highest degree in university" .)

I've seen this clue in The Times.

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