The Trade Agreement quest begins by talking to the Nopon Warawa in the Commercial District (East Melville Street). She'll give you a Bronze Blatta Card to get started.
Trade the Bronze Blatta Card for a Bronze Cinicula Card. For that, you'll have to talk to Liviana in the Commercial District (East of North Founders Street), close to where Yelv usually hangs out.
Find the Nopon Pirapira in the Commercial District (East of West Melville Street, behind Pauline's "Restaurant Rosemoss" and Coco & Jo's "Ewen Lewis") next to some dumpsters. She'll trade her Silver Mortifole Card for your Bronze Cinicula Card. You'll also need 5 Coaletri and 2 Meteo Eater, both are Collectibles found in Primordia.
Your next trading partner is the Ma-non Capsica on the Ma-non Ship (Northeast of Starboard, upper level, eating Pizza at a table with a bunch of other Ma-non). She'll take your Silver Mortifole Card in exchange for... a Ma-non Hunting Kit?
Luckily, Wilbur in the Residential District (In the backyard of a villa Southwest of Ishmael Hills, in front of a swimming pool with his secretary Pepper) is willing to give you a Silver Xiphias Card in exchange for your newly acquired Ma-non Hunting Kit.
Finally, talk to the Orphean Ton'barac in the Residential District (Eastmost tennis court at the Sports Complex). He'll want your Silver Xiphias Card in exchange for the Gold Nopopotamus Card he just found.
With the Gold Nopopotamus Card finally in your grasp, it is time to return to Warawa and finish the quest. You may now congratulate yourself for successfully trading one of the most common Copper Blatta Cards for the legendary Gold Nopopotamus Card. Congratulations!