Sailor, famous person, heading off (3)
I believe the answer is:
tar
'sailor' is the definition.
(slang term for a sailor)
'famous person heading off' is the wordplay.
'famous person' becomes 'star' (star can mean a celebrity).
'heading off' means to remove the first letter.
'star' with its initial letter removed is 'TAR'.
(Other definitions for tar that I've seen before include "Viscous bituminous substance" , "Product of burning tobacco" , "Liquid from wood, coal" , "Dark viscous stuff" , "Tobacco residue; sailor" .)