Lorelei is the Vice Director. The actual Director's been the Director for 2000 years, since the start of the Association itself, and is almost never seen (also thought to be more than human). Basically, the Vice Director does most stuff. It's also a post usually reserved for those from the Barthomeloi family, which is also older than the Association. This is without mentioning all the politics that goes into everything, or the constant political power struggles between the hundreds of family Heads and the Heads of the various departments.
Short answer bloble (odd auto correct brought up your name as a default word) Rin was appointed by Saber because illuminati (previously a cabal established to await the return of king Arthur) controlled and established the association in the first place and immediately handed Saber authority over the association.
what
that's just what
Saber isn't even a mage though.
Also the association is older than Saber. She was alive anywhere from 300 something AD to the 1400s, and it's at least 2000 years old. So it couldn't have been established for her, since she hadn't even been born at that time.
