A quiet guardian, that's obvious (8)
I believe the answer is:
apparent
'obvious' is the definition.
(similar in meaning)
'a quiet guardian' is the wordplay.
'quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'guardian' becomes 'parent'.
'a'+'p'+'parent'='APPARENT'
'that's' acts as a link.
(Other definitions for apparent that I've seen before include "Pane part may be quite obvious" , "Obvious; seemingly true" , "Visible - plain - presumable" , "See 1" , "Evident, manifest" .)