Hav is a sergeant in Amaram's army. Amaram sends the new recruits to him, including Kaladin and Tien. He seems to have been in charge of the new recruits in the army.
Hav harassed the "lad" (i.e., Shallan in disguise) as s/he began to infiltrate the perimeter of Amaram's manor. He insists that from then on that s/he report at the guard posts when s/he visits and then waves her/him on through.
Hav taught Kaladin how to punch:
Thumb outside of his fist, Kaladin connected with the first two knuckles of his hand across Roshone's cheekbone, then followed through to slide across the front of the face. Rarely had he delivered such a perfect punch. It barely even hurt his fist.