Furious to discover affair (8)
I believe the answer is:
seething
'furious' is the definition.
(I've seen this before)
'discover affair' is the wordplay.
'discover' becomes 'see' ('see' can be a synonym of 'discover').
'affair' becomes 'thing' ('thing' can be a synonym of 'affair').
'see'+'thing'='SEETHING'
'to' is the link.
(Other definitions for seething that I've seen before include "Bubbling, perhaps with rage" , "Observe object - bubbling with rage" , "making one very angry" , "Extremely angry" , "Having extreme and barely suppressed anger" .)