Bird with small back found in the mine (6)
I believe the answer is:
peewit
'bird' is the definition.
(peewit is a kind of bird)
'small back found in the mine' is the wordplay.
'small' becomes 'wee' (Scottish term for small).
'back' says the letters should be written backwards.
'found in' indicates putting letters inside.
'the mine' becomes 'pit' (down the pit).
'wee' in reverse letter order is 'eew'.
'eew' placed within 'pit' is 'PEEWIT'.
'with' is the link.
(Other definitions for peewit that I've seen before include "Kind of plover; let it weep" , "Northern lapwing" , "Lapwing turned up in a wee pit" , "Does it weep, this bird?" , "Lapwing - ie wept (anag)" .)