Predator in tavern immediately left (4,3)
I believe the answer is:
barn owl
'predator' is the definition.
(barn owl is a kind of predator)
'tavern immediately left' is the wordplay.
'tavern' becomes 'bar' (I've seen this before).
'immediately' becomes 'now' (I've seen this before).
'left' becomes 'l' (common abbreviation).
'bar'+'now'+'l'='BARN-OWL'
'in' acts as a link.
(Other definitions for barn owl that I've seen before include "Flier" , "Large bird of prey" , "Countryside bird" , "Large hunting bird" , "Mottled buff and white night bird" .)