A quiet Dad is obvious (8)
I believe the answer is:
apparent
'obvious' is the definition.
(similar in meaning)
'a quiet dad' is the wordplay.
'quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'dad' becomes 'parent'.
'a'+'p'+'parent'='APPARENT'
'is' acts as a link.
(Other definitions for apparent that I've seen before include "Obvious, evident" , "Conspicuous" , "Evident or seeming to be" , "Seeming true; obvious" , "Seeming real or true" .)