I'd start to inveigh against unusually coy stupidity (6)
I believe the answer is:
idiocy
'stupidity' is the definition.
(I've seen this before)
'i'd start to inveigh against unusually coy' is the wordplay.
'start to' suggests taking the first letters.
'against' means one lot of letters go next to another.
'unusually' indicates anagramming the letters.
The first letter of 'inveigh' is 'i'.
'coy' with letters rearranged gives 'ocy'.
'id'+'i'+'ocy'='IDIOCY'
(Other definitions for idiocy that I've seen before include "Stupid act" , "Foolishness, asininity" , "Predatory seabird" , "Abject stupidity" , "Complete folly" .)