Very close to stalemate (4,3)
I believe the answer is:
dead end
'to stalemate' is the definition.
(thesaurus)
'very close' is the wordplay.
'very' becomes 'dead' (dead can mean very or absolutely, eg 'dead wrong').
'close' becomes 'end' (I've seen this in another clue).
'dead'+'end'='DEAD END'
(Other definitions for dead end that I've seen before include "A blind alley, sounds moribund" , "Blind alley, closed passage" , "Situation with no way forward" , "A blind alley, point of no further progress" , "Where no progress can be made" .)