Suraya Hawthorne is the vendor in Destiny 2 that deals with Clan progression. She is located at the Farm once you unlock her and at the Tower once you complete the game.
Clan objectives can be completed individually to progress ranking toward your clan level. Almost all activities in the game can net you experience towards your Banners (clan). You will receive a Luminous Engram every time you reach your Weekly Personal Contribution (5,000 EXP), complete a match in the Crucible, complete a Nightfall, complete a Raid or complete a card in the Trials of the Nine. Suraya Hawthorne will be holding your engram for you. There is no steady lootpool for Luminous Engram.
You can check out the shifting lootpool by pressing or on the Faction Reward Engram while speaking to Suraya Hawthorne.