At the end of Reaver of the South, you’ll have the option to kill Fulke’s Champion now or tell him to send a message to Fulke. It doesn’t matter which you choose in terms of the progression of the story, but if you let him go you’ll need to fight him again during Storming the Walls. When the choice arrives, you’ll have the following dialogue options:
Eivor grants the wish of the Champion, and you finish him off.
“Take a message to Fulke.”
The Champion tells Eivor they’ll inform Fulke that her opponent is a weakling who doesn’t have the stomach to finish what they start. You’ll have to fight The Champion again later.