Recording of affair entrapping one (6)
I believe the answer is:
filing
'recording' is the definition.
(filing is a kind of recording)
'affair entrapping one' is the wordplay.
'affair' becomes 'fling' (I have seen 'Brief affair' mean 'fling' so perhaps 'affair' could also mean 'fling').
'entrapping' indicates putting letters inside.
'one' becomes 'i' (Roman numeral).
'fling' going around 'i' is 'FILING'.
'of' is the link.
(Other definitions for filing that I've seen before include "Arranging documents methodically" , "Recording" , "- - cabinet" , "Clerical work (done by metal workers?)" .)