The Sha'tar TIps
The primary way of gaining reputation with the Sha'tar is by running the instances of Tempest Keep, as there are less quests that grant Sha'tar reputation than most other factions.

While gaining Aldor or Scryer reputation from the repeatable quests for those factions, you will also gain a small amount of Sha'tar reputation. However, you will stop gaining Sha'tar reputation for the Aldor/Scryer turn-ins at the end of Friendly Sha'tar.

Most of your Sha'tar reputation will be earned in the Tempest Keep dungeons of Mechanar, Botanica, and Arcatraz. You can also run these dungeons in Heroic mode for additional reputation gains.