Varin was the sword instructor at Kaer Morhen, who was most likely killed during the massacre at Kaer Morhen.
As Geralt explored the bastion where children were trained prior to the Trial of the Grasses, several flashbacks could be seen using Keira's lamp. In the flashbacks Varin was depicted as a ruthless, demanding instructor, pushing the children to their limits. During the massacre at Kaer Morhen it's unknown if he was murdered along with the children and mages, though it can be safely assumed so as it's stated Vesemir was the only one to survive the assault.