Left in nest — no small bird (6)
I believe the answer is:
linnet
'bird' is the definition.
(linnet is a kind of bird)
'left in nest no small' is the wordplay.
'left' becomes 'l' (common abbreviation**).
'no' indicates named letters should be taken away.
'small' becomes 's' (abbreviation - e.g. clothes size).
'nest' with 's' removed is 'net'.
'l'+'in'+'net'='LINNET'
(Other definitions for linnet that I've seen before include "Songbird in Lent" , "Common finch" , "Finch so named because it feeds on flax" , "A little bird" , "Yeats's song-bird" .)