Boasting without publicity is well done (5)
I believe the answer is:
bravo
'well done' is the definition.
(I've seen this before)
'boasting without publicity' is the wordplay.
'boasting' becomes 'bravado' (I've seen this before).
'without' indicates named letters should be taken away.
'publicity' becomes 'ad' (short for advertisement).
'bravado' with 'ad' taken away is 'BRAVO'.
'is' is the link.
(Other definitions for bravo that I've seen before include "B in radio communications" , "Cry of approval" , "congratulations" , "Expression of approval" , "How broadcaster might begin birthday" .)