Putting on record one caught in affair (6)
I believe the answer is:
filing
'putting on record' is the definition.
('file' can be a synonym of 'put on record')
'one caught in affair' is the wordplay.
'one' becomes 'I' (Roman numeral).
'caught in' is an insertion indicator.
'affair' becomes 'fling' (a fling is a romantic affair).
'i' put within 'fling' is 'FILING'.
(Other definitions for filing that I've seen before include "Clerical work (done by metal workers?)" , "Arranging documents methodically" , "- - cabinet" , "Recording" .)