The Allegiance quest should be available if you haven't done it already, but there is currently a bug with the step that requires you to visit Spider that is preventing progress in the quest. They're aware, and are investigating. While you should eventually be able to complete the quest, the weekly loyalty packages you would get for completing the quest were removed at the start of the new season. The Invitations of the Nine can still be completed as well. Visit Xur each week to buy an invitation, and as long as you complete it before daily reset on Thursday, Xur will have a new invitation available the following day, at reset on Friday, until you finish the final invitation.