Head’s briefly g-gone back home (6)
I believe the answer is:
noggin
'head's' is the definition.
(noggin is a kind of head)
'briefly g-gone back home' is the wordplay.
'briefly' means to remove the last letter.
'back' says the letters should be written backwards.
'home' becomes 'in' ('he's home' can mean 'he's in').
'g'+'gone'='ggone'
'ggone' with its last letter taken off is 'ggon'.
'ggon' in reverse letter order is 'nogg'.
'nogg'+'in'='NOGGIN'
(Other definitions for noggin that I've seen before include "Small measure of spirits or mug" , "Human head -- small drink" , "Small measure of spirits or slangy head" , "Small bottle of spirits" , "Gill usually" .)