Deadlock that is broken by politician: fool! (7)
I believe the answer is:
impasse
'deadlock' is the definition.
(I know that deadlock can be written as impasse)
'that is broken by politician fool' is the wordplay.
'that is' becomes 'ie' (short for Latin 'id est', 'that is').
'broken by' means one lot of letters goes inside another (inserted letters break into the word).
'politician' becomes 'MP' (Member of Parliament).
'fool' becomes 'ass' (both can mean a stupid person).
'mp'+'ass'='mpass'
'ie' enclosing 'mpass' is 'IMPASSE'.
(Other definitions for impasse that I've seen before include "There's no way past it" , "Deadlock or stand-off" , "'Deadlock, stalemate (7)'" , "'Deadlock, no progress can be made (7)'" , "block" .)