Authorise mother to come back first - that's agreeable (8)
I believe the answer is:
amenable
'agreeable' is the definition.
(synonyms)
'authorise mother to come back first' is the wordplay.
'authorise' becomes 'enable' (I've seen this in another clue).
'mother' becomes 'ma' (Ma is another word for mother or mum).
'to come back' is a reversal indicator.
'first' means one lot of letters go next to another.
'ma' reversed gives 'am'.
'enable' after 'am' is 'AMENABLE'.
'that's' acts as a link.
(Other definitions for amenable that I've seen before include "Accommodating; flexible" , "Willing to be guided, being nameable" , "Nameable as being subject to the law" , "Ready to accept" , "Prepared to fall in with others' plans" .)