Crossword Genius

It makes the heart grow fonder briefly, being away from church (7)

Ross

I believe the answer is:

absence

I'm a little stuck... Click here to teach me more about this clue!

'it makes the heart grow fonder' is the definition.
(I've seen this before)

'briefly being away from church' is the wordplay.
I cannot quite see how this works, but
'being' could be 'b' (B is an example) and 'b' is found within the answer.
'away' could be 'a' (abbreviation as used in sports fixtures) and 'a' is located in the answer.
'church' could be 'ce' (abbreviation for Church of England) and 'ce' is found within the answer.
The remaining letters 'sen' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for absence that I've seen before include "Non-presence" , "What supposedly makes the heart grow fonder?" , "Failure to show" , "It makes the heart grow fonder, they say" , "Lack (of something)" .)

I've seen this clue in the Irish Times and the Irish Times (Crosaire).
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