Heading off, bald eagle approaching unknown island (8)
I believe the answer is:
alderney
'island' is the definition.
(I've seen this before)
'heading off bald eagle approaching unknown' is the wordplay.
'heading off' means to remove the first letter.
'eagle' becomes 'erne' (erne is a kind of eagle).
'approaching' says to put letters next to each other.
'unknown' becomes 'y' (algebra).
'bald' with its first letter removed is 'ald'.
'ald'+'erne'+'y'='ALDERNEY'
(Other definitions for alderney that I've seen before include "Cow, perhaps" , "One of Channel Islands" , "Third largest of the Channel Islands" , "Channel isle" , "A Channel Island" .)