Awfully sly men, extremely unchaste and improper (8)
I believe the answer is:
unseemly
'improper' is the definition.
(similar in meaning)
'awfully sly men extremely unchaste' is the wordplay.
'awfully' indicates an anagram.
'extremely' says to hollow out the word (remove centre letters) (letters on the extremes of the word are used).
'unchaste' with its middle removed is 'ue'.
'sly'+'men'+'ue'='slymenue'
'slymenue' with letters rearranged gives 'UNSEEMLY'.
'and' is the link.
(Other definitions for unseemly that I've seen before include "Inappropriate" , "Disreputable" , "Indecent" , "Not decorous or fitting" , "Not quite the thing" .)