Queen known for beat (4)
I believe the answer is:
rout
'for beat' is the definition.
(routing is a kind of beating)
'queen known' is the wordplay.
'queen' becomes 'r' (abbreviation for regina, e.g. in ER ).
'known' becomes 'out' (as in news which is 'out').
'r'+'out'='ROUT'
(Other definitions for rout that I've seen before include "Drubbing" , "clobber" , "snore" , "Big defeat" , "Headlong flight" .)