Influence American to abandon holiday passion (8)
I believe the answer is:
leverage
'influence' is the definition.
(thesaurus)
'american to abandon holiday passion' is the wordplay.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'to abandon' indicates named letters should be taken away.
'holiday' becomes 'leave' (I've seen this before).
'passion' becomes 'rage' ('rage' can be a synonym of 'passion').
'leave' with 'a' taken out is 'leve'.
'leve'+'rage'='LEVERAGE'
(Other definitions for leverage that I've seen before include "financial advantage" , "Economic clout" , "Purchase" , "Power -- advantage" , "Power to act effectively" .)