Having bargained for housing, old rogue coughed up (12)

I believe the answer is:

expectorated

'coughed up' is the definition.
('expectorate' can be a synonym of 'cough up')

'having bargained for housing old rogue' is the wordplay.
I cannot quite see how this works, but
'old' could be 'ex' and 'ex' is found within the answer.
This may be the basis of clue (or it may be nonsense).

I've seen this clue in The Guardian.

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