Very quiet song a prior put on (7)
I believe the answer is:
applied
'put on' is the definition.
(I've seen this in another clue)
'very quiet song a prior' is the wordplay.
'very quiet' becomes 'pp' (musical abbreviation for pianissimo).
'song' becomes 'lied' (type of German song).
'prior' says to put letters next to each other.
'pp'+'lied'='pplied'
'pplied' after 'a' is 'APPLIED'.
(Other definitions for applied that I've seen before include "Type of science" , "Employed" , "Responded to job ad" , "Put into practice or requested" , "put to practical use" .)