Chaffinch initially rebuilt nest in shed for horse (8)
I believe the answer is:
chestnut
'horse' is the definition.
(chestnut is a kind of horse)
'chaffinch initially rebuilt nest in shed' is the wordplay.
'initially' suggests taking the first letters.
'rebuilt' indicates anagramming the letters.
'in' is an insertion indicator.
'shed' becomes 'hut' (I've seen this before**).
The initial letter of 'chaffinch' is 'c'.
'nest' anagrammed gives 'estn'.
'estn' placed into 'hut' is 'hestnut'.
'c'+'hestnut'='CHESTNUT'
'for' acts as a link.
(Other definitions for chestnut that I've seen before include "Sweet -; horse -; water -" , "Reddish-brown colour" , "Item for stuffing" , "Laughably predictable" , "Deep reddish-brown" .)