Relaxed at home because mother left (8)
I believe the answer is:
informal
'relaxed' is the definition.
(I've seen this before)
'home because mother left' is the wordplay.
'home' becomes 'in' ('he's home' can mean 'he's in').
'because' becomes 'for' (I've seen this in other clues).
'mother' becomes 'ma' (Ma is another word for mother or mum).
'left' becomes 'l' (common abbreviation).
'in'+'for'+'ma'+'l'='INFORMAL'
'at' is the link.
(Other definitions for informal that I've seen before include "Casual, not official" , "Casual and unceremonious" , "If normal, be casual and without ceremony" , "Casual or unofficial" , "Cosy -- loose" .)