'Orrible situation returning -- flier gets round it -- that brings relief (10)
I believe the answer is:
alleviator
'that brings relief' is the definition.
(something which alleviates or relieves)
''orrible situation returning flier gets round it' is the wordplay.
''orrible situation' becomes ''ell' ('hell' - hell can mean a horrible or difficult situation - said with a cockney accent, dropping the 'H', like 'horrible situation' was).
'returning' is a reversal indicator.
'flier' becomes 'aviator' (synonyms).
'gets round it' means one lot of letters goes inside another.
'ell' reversed gives 'lle'.
'lle' placed into 'aviator' is 'ALLEVIATOR'.
(Other definitions for alleviator that I've seen before include "could make things easier" , "Provides relief" .)