A very quiet final period for the tail? (9)
I believe the answer is:
appendage
'the tail?' is the definition.
(thesaurus)
'a very quiet final period' is the wordplay.
'very quiet' becomes 'pp' (musical abbreviation for pianissimo).
'final' becomes 'end' (synonyms).
'period' becomes 'age' (age is a kind of period).
'a'+'pp'+'end'+'age'='APPENDAGE'
'for' acts as a link.
(Other definitions for appendage that I've seen before include "Something attached to a larger thing" , "It's added or attached to a larger or more important part" , "Attached item" , "An outgrowth" , "Addendum" .)