Lawmen had issued a wanted bulletin for Clarke on June 8.
According to police, they were on patrol along Lower Gills Road, St Michael when they encountered a vehicle they had reason to stop.
As the vehicle stopped, two occupants got out and fled.
A third individual who was armed with a firearm engaged police and officers fired back to defend themselves.
The man, Clarke, was injured and subsequently pronounced dead at the scene by a medical doctor.
Police are continuing investigations.