Old sort of French-style boarding house on Exeter's outskirts (9)

I believe the answer is:

pensioner

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'old sort of french-style' is the definition.
I can't judge whether this defines the answer.

'boarding house on exeter's outskirts' is the wordplay.
'boarding house' becomes 'pension' (I've seen this before).
'on' is a charade indicator (letters next to each other).
'outskirts' suggests removing the centre (I've seen 'outskirts of' mean this).
'exeter' with its middle removed is 'er'.
'pension'+'er'='PENSIONER'

Can you help me to learn more?

(Other definitions for pensioner that I've seen before include "Maybe Chelsea man" , "senior citizen" , "Former worker" , "beneficiary of fund" , "One is older and paid so they don't have to work" .)

I've seen this clue in The Independent.

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