Dismiss expert screening river fun run (4,4)
I believe the answer is:
sack race
'fun run' is the definition.
'dismiss expert screening river' is the wordplay.
'dismiss' becomes 'sack' ('sack' can be a synonym of 'dismiss').
'expert screening river' becomes 'race' (I can't explain this - if you can you should give a lot more credence to this answer).
'sack'+'race'='SACK-RACE'
(Other definitions for sack race that I've seen before include "athletics contest" , "'Novelty competition where entrants run with their feet in a bag (4,4)'" , "jumping event" , "event - with 10d" , "Novelty competition on school sports day" .)