Vain Englishman and American crossing river (7)
I believe the answer is:
pompous
'vain' is the definition.
(I've seen this before)
'englishman and american crossing river' is the wordplay.
'englishman' becomes 'pom' (pom is an Australian term for an English person).
'and' is a charade indicator (letters next to each other).
'american' becomes 'us' (abbreviation for United States).
'crossing' indicates putting letters inside.
'river' becomes 'Po' (Italian river).
'pom'+'us'='pomus'
'pomus' going around 'po' is 'POMPOUS'.
(Other definitions for pompous that I've seen before include "Proud" , "Vain" , "Affectedly self-important" , "Arrogant" , "Grandly self-important" .)