Manager disheartened, possibly, by a European (6)
I believe the answer is:
german
'a european' is the definition.
(I know that German is a type of european)
'manager disheartened possibly' is the wordplay.
'disheartened' says to hollow out the word (remove centre letters) (the middle or heart is removed).
'possibly' is an anagram indicator.
'manager' with its middle taken out is 'manger'.
'manger' with letters rearranged gives 'GERMAN'.
'by' acts as a link.
(Other definitions for german that I've seen before include "This national rang me up" , "European national" , "foreign" , "Alsatian" , "Helmut?" .)