" Q. How can I get a sponsor?

A. You can get a sponsor by meeting us in Tel'Ruid. You'll eventually get to know someone who will volunteer to be your sponsor and take you through the application process. As a potential applicant, you must gain a member's Trust, Respect, and Friendship before they'll be your sponsor. Even if you feel that those three are met, be patient. These things take time. For more information please check our Guild Charter."

So you see the Tel'Mithrim is a group of very close friends. Until you have become a very close friend of another Tel'Mithrim member you will not become a member yourself.
How long does it take to become close friend with someone? Well, how long did it take you to become close friends with your Real life close friends? Perhaps a year? two? three?
It might very well be the same kind of wait you are going through if you wish to enter the Tel'Mithrim.

But you could start by going to their festival, which runs these days.

-Edge