Shot on street in engagement (5)
I believe the answer is:
tryst
'engagement' is the definition.
(tryst is a kind of engagement)
'shot on street' is the wordplay.
'shot' becomes 'try' (I've seen this in other clues).
'on street' becomes 'st' (I've seen this in other clues).
'try'+'st'='TRYST'
'in' acts as a link.
(Other definitions for tryst that I've seen before include "Romantic assignation" , "Lump (of gold, etc)" , "Rendezvous with lover" , "Lovers' assignation" , "Romantic rendezvous (literary)" .)