Cheekiness of worker — brave! (7)
I believe the answer is:
gallant
'brave' is the definition.
(similar in meaning)
'cheekiness of worker' is the wordplay.
'cheekiness' becomes 'gall'.
'of worker' becomes 'ant' (I am not sure about this - if you are sure you should believe this answer much more).
'gall'+'ant'='GALLANT'
(Other definitions for gallant that I've seen before include "Dashing, debonair young man" , "Dandy" , "Brave and chivalrous like knight of old" , "Brave and honourable" , "Brave; courteous" .)