Being prudish and upset I'd start storing delicate material (6-5)
I believe the answer is:
strait-laced
'being prudish' is the definition.
('strait-laced' can be a synonym of 'prudish')
'upset i'd start storing delicate material' is the wordplay.
'upset' indicates an anagram.
'storing' indicates putting letters inside.
'delicate material' becomes 'lace' (I've seen this before).
'id'+'start'='idstart'
'idstart' is an anagram of 'straitd'.
'straitd' placed around 'lace' is 'STRAIT-LACED'.
'and' acts as a link.
(Other definitions for strait-laced that I've seen before include "Having strict morals" , "Narrow-minded" , "Prudish" , "Strictly moral" .)