Muse, on reflection unwilling to supply waterproof material (8)
I believe the answer is:
oilcloth
'waterproof material' is the definition.
(I've seen this before)
'muse on reflection unwilling' is the wordplay.
'muse' becomes 'Clio' (muse of history in Greek myth).
'on reflection' is a reversal indicator.
'unwilling' becomes 'loth' (similar in meaning).
'clio' reversed gives 'oilc'.
'oilc'+'loth'='OILCLOTH'
'to supply' acts as a link.
(Other definitions for oilcloth that I've seen before include "Canvas" , "may hold off the showers" , "Waterproof material" , "Waterproof fabric" , "not to be used for watercolours!" .)