Cheeky? I'm put outside study (8)
I believe the answer is:
impudent
'cheeky?' is the definition.
(I've seen this before)
'i'm put outside study' is the wordplay.
'outside' means one lot of letters goes inside another.
'study' becomes 'den' (term for a study or office).
'put' going around 'den' is 'pudent'.
'im'+'pudent'='IMPUDENT'
(Other definitions for impudent that I've seen before include "Cheeky, disrespectful" , "Lippy" , "Saucy" , "Audacious" , "impolite" .)