Jobless heading off, possibly for a Greek island (6)
I believe the answer is:
lesbos
'a greek island' is the definition.
(I've seen this before)
'jobless heading off possibly' is the wordplay.
'heading off' means to remove the first letter.
'possibly' is an anagram indicator.
'jobless' with its initial letter taken off is 'obless'.
'obless' anagrammed gives 'LESBOS'.
'for' acts as a link.
(Other definitions for lesbos that I've seen before include "Island, home of Sappho" , "Greek island, birthplace of Sappho" , "Greek island -- home of 3" , "Jot" .)