Undiplomatic cast’s let off (8)
I believe the answer is:
tactless
'undiplomatic' is the definition.
('tactless' can be a synonym of 'undiplomatic')
'cast's let off' is the wordplay.
'off' indicates an anagram.
'casts'+'let'='castslet'
'castslet' with letters rearranged gives 'TACTLESS'.
(Other definitions for tactless that I've seen before include "Showing no sensitivity to others" , "Showing insensitivity to others" , "Gaffe-prone" , "Maladroit" , "Lacking sensitivity in dealing with others" .)