Gent heading off with European band's recording (8)
I believe the answer is:
entering
'recording' is the definition.
('enter' can be a synonym of 'record')
'gent heading off with european band's' is the wordplay.
'heading off' means to remove the first letter.
'with' means one lot of letters go next to another.
'european' becomes 'e' (abbreviation e.g. EU).
'band' becomes 'ring' ('ring' can be a synonym of 'band'**).
'gent' with its initial letter taken away is 'ent'.
'ent'+'e'+'ring'='ENTERING'
(Other definitions for entering that I've seen before include "Going inside" , "Starting" , "Coming in" , "Going/coming in" .)