Humdrum character given note by European national (7)
I believe the answer is:
mundane
'humdrum' is the definition.
(I've seen this before)
'character given note by european national' is the wordplay.
'character given' becomes 'mu' (Greek letter. I am not sure about the 'given' bit.).
'note' becomes 'n' (abbreviation).
'by' is a charade indicator (letters next to each other).
'european national' becomes 'dane' (someone from Denmark).
'mu'+'n'+'dane'='MUNDANE'
(Other definitions for mundane that I've seen before include "Banal; earthly" , "Lacking excitement; worldly" , "Unexciting; of this world" , "Boring" , "Drab" .)