Written assurance offered as cautious about storm (8)
I believe the answer is:
warranty
'written assurance offered' is the definition.
(assurance offered by a manufacturer)
'cautious about storm' is the wordplay.
'cautious' becomes 'wary' (similar in meaning).
'about' means one lot of letters goes inside another.
'storm' becomes 'rant' (both can mean to rage).
'wary' placed around 'rant' is 'WARRANTY'.
'as' acts as a link.
(Other definitions for warranty that I've seen before include "pledge" , "Undertaking (as to quality)" , "Certificate" , "cover provided" , "Guarantee given to a purchaser" .)