Jessup first joined the Grenville Militia in 1829 as an Ensign eventually rising to Captain, and had commanded the Prescott Volunteer Battalion at the Battle of the Windmill in 1838.
In 1829, Jessup began his service with the Grenville Militia as an ensign before advancing to captain rank. He commanded the Prescott Volunteer Battalion during the Battle of the Windmill in 1838.