Spinster destroyed odd mail (3,4)
I believe the answer is:
old maid
'spinster' is the definition.
(synonyms)
'destroyed odd mail' is the wordplay.
'destroyed' is an anagram indicator.
'odd'+'mail'='oddmail'
'oddmail' anagrammed gives 'OLD MAID'.
(Other definitions for old maid that I've seen before include "She's elderly and unmarried" , "Spinster - card game" , "Obsolete expression for elderly unmarried woman" , "Pejorative term for elderly unmarried woman" , "never taken from the shelf?" .)