Back in Galloway, having left without permission (4)
I believe the answer is:
awol
'left without permission' is the definition.
(absent without leave)
'back in galloway having' is the wordplay.
'back' says the letters should be written backwards.
'in' says the answer is hidden in the clue.
'lowa' can be found hidden inside 'galloway having'.
'lowa' in reverse letter order is 'AWOL'.
(Other definitions for awol that I've seen before include "Missing without permission" , "Army offence of being missing from duty, briefly" , "gone missing" , "Absent without permission, in short" , "unaccounted for" .)