A quiet Mum or Dad, that’s obvious (8)
I believe the answer is:
apparent
'obvious' is the definition.
(similar in meaning)
'a quiet mum or dad' is the wordplay.
'quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'mum or dad' becomes 'parent' (I've seen this before).
'a'+'p'+'parent'='APPARENT'
'that's' is the link.
(Other definitions for apparent that I've seen before include "That may be seen" , "See 1" , "Evident, manifest" , "Seeming true; obvious" , "Obvious, evident" .)