Decline to live by American rule (7)
I believe the answer is:
forbear
'decline' is the definition.
(thesaurus)
'to live by american rule' is the wordplay.
'to' becomes 'for'.
'live' becomes 'be' ('be' can be a synonym of 'live'**).
'by' says to put letters next to each other.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'rule' becomes 'r' (legal abbreviation).
'for'+'be'+'a'+'r'='FORBEAR'
(Other definitions for forbear that I've seen before include "Hold back" , "Abstain" , "Be patient" , "Refrain from doing something" .)