Speak with Squire Danny to summon your opponent. Once you have defeated the Argent Champion, return to Eressea Dawnsinger at the Argent Tournament Grounds.
If you lose your lance, you can get another from any of the Lance Racks near the stables or in the Sunreaver Pavilion.
Argent Champion defeated
You are nearly ready to compete in the grand melee. To prove yourself worthy of this honor, you must defeat a champion of the Argent Crusade.
Go to the stables outside the pavilion, equip your lance, and mount up. Speak to Squire Danny at the Argent Valiants' Ring on the western edge of the grounds. The squire will call out your opponent when you're ready.
After the battle is concluded, we will speak of the outcome.
You have proven yourself worthy of the title of champion, <name>. You will compete at the tournament's highest level, riding in the grand melee and crushing the competition under the banner of Silvermoon.