There's two important effects I'm aware of.
Achieving a rank of Elite in Combat (or Trade, or Exploration, or CQC) will give you access to the Shinrarta Dezhra system.
The Shinrarta Dezhra system is particularly important because it is home to the Jameson Memorial station, which orbits Founders World. Jameson Memorial is most notable for always having all player-purchasable ships and modules available for sale. An added bonus there is that ships and modules are sold at a 10% discount.
It is possible to get access to this system without having an Elite rank, but only if you backed the Kickstarter campaign for the game.
Some Engineers require certain Pilots Federation ranks for you to gain access. Those known to have such requirements at this time are:
- Felicity Farseer, requiring Exploration rank Scout or higher.
- Broo Tarquin, requiring Combat rank of Competent or higher.
- Didi Vatermann, requiring Trade rank of Merchant or higher.