Desperate character, eastern European (4)
I believe the answer is:
dane
'european' is the definition.
(someone from Denmark)
'desperate character eastern' is the wordplay.
'desperate character' becomes 'dan' (Desperate Dan the comic character).
'eastern' becomes 'e'.
'dan'+'e'='DANE'
(Other definitions for dane that I've seen before include "Hamlet was one" , "Hamlet, say" , "See 7 Down" , "Native of Copenhagen, for instance" , "Great - - , dog" .)