Provoke former top judge about British (10)
I believe the answer is:
exacerbate
'provoke' is the definition.
(I've seen this before)
'former top judge about british' is the wordplay.
'former' becomes 'ex'.
'top judge' becomes 'acerate' (I can't justify this - if you can you should believe this answer much more).
'about' is an insertion indicator.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'acerate' enclosing 'b' is 'acerbate'.
'ex'+'acerbate'='EXACERBATE'
Can you help me to learn more?
(Other definitions for exacerbate that I've seen before include "Provoke" , "Worsen" , "Make (a bad thing) worse" .)