Unfortunate friar in A&E finding cost going up? (7)
I believe the answer is:
airfare
'cost going up?' is the definition.
(cost of travelling up in the air)
'unfortunate friar in ae' is the wordplay.
'unfortunate' indicates an anagram.
'in' indicates putting letters inside.
'friar' is an anagram of 'irfar'.
'irfar' placed into 'ae' is 'AIRFARE'.
'finding' is the link.
(Other definitions for airfare that I've seen before include "The cost of travelling" , "flight damage" , "Price of a flight" , "One won't catch a plane without it" , "Charge for flight" .)