Thoroughly explore musical ability in school (6)

I believe the answer is:

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'thoroughly explore' is the definition.
'search' can be an answer for 'explore' (synonyms). I'm unsure of the 'thoroughly' bit.

'musical ability in school' is the wordplay.
'musical ability' becomes 'ear' (I've seen this in another clue).
'in' means one lot of letters goes inside another.
'school' becomes 'sch' (common abbreviation).
'ear' placed inside 'sch' is 'SEARCH'.

Can you help me to learn more?

(Other definitions for search that I've seen before include "Seek (out); hunt (for)" , "Examine (to find something)" , "Frisk" , "Fish about" , "Look for something or someone, perhaps chaser" .)

I've seen this clue in The Times.

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