Set off on a journey with English tree hugger consumed by Mediterranean (8)
I believe the answer is:
embarked
'set off on a journey' is the definition.
'english tree hugger consumed by mediterranean' is the wordplay.
'english' becomes 'e' (abbreviation).
'tree hugger' becomes 'bark'.
'consumed by' is an insertion indicator.
'mediterranean' becomes 'med' (I've seen this in other clues).
'bark' inserted into 'med' is 'mbarked'.
'e'+'mbarked'='EMBARKED'
'with' is the link.
(Other definitions for embarked that I've seen before include "Set out on a voyage" , "Having set sail" , "Got on" , "Began (on project)" , "Went on board ship or plane" .)