When you activate a sponsorship, you get item cards after each game. After a certain amount of cards are acquired you can use Coins to upgrade them. Upgrading increases the stat boost as well as unlocking different color variants at specific levels for that apparel.
To Upgrade apparel, simply tap your profile photo, then the Apparel tab, then Edit Apparel at the bottom. Select whichever item you would like to upgrade and if it is equipped, the upgrade button will be just below the picture of the item. If it is on the comparison screen(the item is not equipped) then it will still appear below the item's image.
Click the following link for a deeper look into apparel...
Apparel Megathread