One and only constant is spy chief’s impropriety (8)
I believe the answer is:
solecism
'impropriety' is the definition.
(thesaurus)
'one and only constant is spy chief's' is the wordplay.
'one and only' becomes 'sole' (synonyms).
'constant' becomes 'c' (mathematical abbreviation).
'spy chief' becomes 'm' (M is the head of MI6 in the James Bond series).
'sole'+'c'+'is'+'m'='SOLECISM'
(Other definitions for solecism that I've seen before include "Ungrammatical use of words - breach of good manners" , "Social gaffe" , "Incongruity" , "Error in grammar or manners" , "Absurdity" .)