At home, cut up coat: at the edges it's woolly (7)
I believe the answer is:
inexact
'it's woolly' is the definition.
(I've seen this before)
'at home cut up coat at the edges' is the wordplay.
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'cut' becomes 'axe' (both can mean to cancel or remove).
'up' is a reversal indicator (in down clue: letters go upwards).
'at the edges' means to remove the middle letters.
'coat' with its centre taken out is 'ct'.
'axe' backwards is 'exa'.
'in'+'exa'+'ct'='INEXACT'
(Other definitions for inexact that I've seen before include "not precisely correct" , "Not quite accurate" , "Fuzzy, muddled" , "Not quite right" , "Not precise, like some sciences" .)