You can unlock a variety of costumes by satisfying certain conditions, including having saves and Uplay investments from previous games in the series that are available on the platform. The available costumes and the corresponding conditions required are listed below.

Altair Robes - Requires data from first Assassin's Creed
Altaïr Ibn-La'Ahad Outfit - Requires Uplay data from 1 prior Assassin's Creed title
Cat Outfit - Purchase required pelts from any general store
Connor Kenway Outfit - Requires Uplay data from 3 prior Assassins Creed titles
Connor Robes - Requires data from Assassin's Creed 3
Edward The Legend Outfit - Play in single-player while wearing Edward's authentic pirate outfit (costs 20 Uplay points)
Ezio Robes - Requires data from Assassin's Creed 2
Hunter Outfit - Craft after purchasing the red howler monkey skin and the white jaguar pelt from any general store
Mayan Outfit - Open the secret door in Tulum after gathering the 16 Mayan stones by completing the Mayan Stelae missions
Stealth Outfit - Complete half of the the Assassin contracts
Templar Outfit - Open the cage in the Great Inagua hideout using keys gained by completing the 16 Templar Hunt missions
The Blades of Toledo Pack - Play in single-player while wearing the Blades of Toledo (costs 30 Uplay points)
The Vengeful Daughter Pack - Access the Lady Black's Vengeful Daughter costume in multiplayer (costs 40 Uplay points)