Encounter with Vagrant horse (4,4)
I believe the answer is:
bump into
'encounter' is the definition.
(synonyms)
'with vagrant horse' is the wordplay.
'with' says to put letters next to each other.
'vagrant' becomes 'bum'.
'horse' becomes 'pinto' (pinto is a kind of horse).
'bum' put next to 'pinto' is 'BUMP INTO'.
(Other definitions for bump into that I've seen before include "meet, unexpectedly" , "Chance upon" , "Unintentionally come across" , "Encounter" , "Come across unexpectedly" .)