In the affair Rita tends to cause annoyance (8)
I believe the answer is:
irritate
'cause annoyance' is the definition.
(I've seen this before)
'in the affair rita tends' is the wordplay.
'in' says the answer is hidden in the clue.
'IRRITATE' is hidden in the letters of 'affair rita tends'.
'to' acts as a link.
(Other definitions for irritate that I've seen before include "Nettle and annoy" , "Annoy, rankle with" , "bug" , "Nark" , "Rattier, I may be annoying" .)