Heading off very much in advance (5)
I believe the answer is:
early
'in advance' is the definition.
(similar in meaning)
'heading off very much' is the wordplay.
'heading off' means to remove the first letter.
'very much' becomes 'dearly'.
'dearly' with its first letter removed is 'EARLY'.
(Other definitions for early that I've seen before include "at start of day" , "Prematurely" , "sooner than expected" , "Before the usual time" , "Forward" .)