Leave former partner to take courses (5)

I believe the answer is:

exeat

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'leave' is the definition.
(I've seen this before)

'former partner to take courses' is the wordplay.
'former partner' becomes 'ex' (an ex-partner).
'to take courses' becomes 'eat' (I can't explain this - if you can you should give a lot more credence to this answer).
'ex'+'eat'='EXEAT'

Can you help me to learn more?

(Other definitions for exeat that I've seen before include "permission to leave" , "Leave of absence" , "Permit for absence" , "Permission to go" , "Permission for absence from school" .)

I've seen this clue in The Times.

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