The Harpy Contract is a Witcher 2 Assassins of Kings Enhanced Edition side-quest available during the second act of the game, if you sided with Iorveth.
The Harpy Contract quest can be activated when visiting the inn in Vergen, if you check the board near the entrance.
While in Upper Aedirn, Geralt was on the lookout for witchers work. When he learned that Vergens authorities had posted a bounty tor thinning the local harpy population, he applied for the job.
First, he decided to learn more about the winged creatures habits, either by exterminating one by one or by reading professional literature about them.
When to start
While playing Hunting Magic
The Harpy Contract side-quest is similar to The Nekker Contract, because to complete it, you need some special items, named Harpy Traps.
Your first goal is to learn how to use them; therefore, you have two options. You can kill several harpies in the Outskirts of Vergen, while you search the area for the first artifact required by Philippa (when you start Hunting Magic), or if you have enough coins, you can purchase a book directly from Felicia Cori at the marketplace, when you purchase the Surgical Kit (for With Flickering Heart side quest).
The book you have to buy is called Harpies Daughters of the Gale.
Either way, after you gather enough information about these beasts you need seven traps. These items can be purchased from Haggard.
If you completed Poker Face: Vergen you already know who Haggard is, since he was your last opponent in the dice poker tournament. Visit him and get the diagram or purchase some traps. Make sure you have seven devices.
Now, when you start Hunting Magic, you will have to travel to the Old Quarry. On your way to the bottom, you will be attacked by many Harpies. Make sure you place some traps on the ground so the beasts can pick them up and carry them to their nests.
The devices will explode, exterminating the harpies.
Additional Harpies can be found inside the quarry, when you look for their queen. Be careful because they are fast and vicious creatures.
After you place seven traps, the quest ends and you can return to Cecil Burdon for your reward.