Without a key that's found in coat on a line (6)
I believe the answer is:
atonal
'without a key' is the definition.
(I've seen this before)
'found in coat on a line' is the wordplay.
'found in' indicates a hidden word.
'ATONAL' can be found hidden inside 'coat on a line'.
'that's' acts as a link.
(Other definitions for atonal that I've seen before include "Not in a key (mus.)" , "Musically, having no established key" , "Keyless" , "(Music) having no established key" , "(Of music) lacking key" .)