Behaviour of European base in grim surroundings (9)
I believe the answer is:
demeanour
'behaviour' is the definition.
('demeanour' can be a synonym of 'behaviour')
'european base in grim surroundings' is the wordplay.
'european' becomes 'e' (abbreviation e.g. EU).
'base' becomes 'mean' ('mean' can be a synonym of 'base'**).
'in' is an insertion indicator.
'grim' becomes 'dour' ('dour' can be a synonym of 'grim').
'surroundings' indicates putting letters inside.
'mean' inserted within 'dour' is 'dmeanour'.
'e' inserted within 'dmeanour' is 'DEMEANOUR'.
'of' is the link.
(Other definitions for demeanour that I've seen before include "Appearance and attitude" , "Outward bearing" , "Manner of behaving towards others" , "Look" , "Conduct" .)