Strengthening, ending trouble, holding European record (9)
I believe the answer is:
deepening
'strengthening' is the definition.
(thesaurus)
'ending trouble holding european record' is the wordplay.
'trouble' is an anagram indicator.
'holding' means one lot of letters goes inside another.
'european' becomes 'E' (abbreviation e.g. EU).
'record' becomes 'EP' (abbreviation for extended play record).
'ending' with letters rearranged gives 'dening'.
'e'+'ep'='eep'
'dening' going around 'eep' is 'DEEPENING'.
(Another definition for deepening that I've seen is " lowering".)