Songstress's first inferior track (5)
I believe the answer is:
spoor
'track' is the definition.
(spoor is a kind of track)
'songstress's first inferior' is the wordplay.
'first' indicates taking the first letters.
'inferior' becomes 'poor' ('poor' can be similar in meaning to 'inferior').
The initial letter of 'songstress' is 's'.
's'+'poor'='SPOOR'
(Other definitions for spoor that I've seen before include "Trace" , "Track of wild animal" , "Animal track, trail" , "Animal track or scent" , "24 [TRAIL]" .)