Spent last season in Dover but headed off early having got too cold, perhaps (12)

I believe the answer is:

overwintered

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'dover but headed off early having got too cold perhaps' is the definition.
I can't tell whether this defines the answer.

'spent last season in' is the wordplay.
'spent last' becomes 'overed' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'season' becomes 'winter' (winter is a season).
'in' indicates putting letters inside.
'overed' enclosing 'winter' is 'OVERWINTERED'.

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I've seen this clue in The Irish Times.

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