You get rep from killing the rares once a day. Each rare can give between 10-15 rep per day.
You will get rep from doing the Patterns Within Patterns quest. It will be changed to a weekly quest starting with Tuesday’s reset. The rewards from it will be adjusted accordingly, so I do not have the new rep amount from that available at this time.
link: Patterns within Patterns - #21 by Linxy
Tuesday’s reset will also open up the new world boss. It will be on a weekly lockout and will provide 200 rep.
Completing the world quests available each day will provide 125 rep per.