After you hit lvl 6 in Fed you can roll up a Klingon, or one of their subservient races, like Gorn, Orion, Naussicaan or you can create your own race. The Klingon starts out as lvl 5, and you have to do some simple and quick 'run around and learn the place' quests before you get to fight. Sort of a mini tutorial.
From there, you can either engage in PvE against NPC Fed fleets or head straight to PvP against other Klingons or Feds. You have to click a button to enter the PvP queu, which as a Klingon has a very low timer; Klingons are usually outnumbered.
I prefer the underdog......so Klingon here i come!
I usually jump back over to my Fed character to play pve. Anytime I want to play pvp I go to my klingon characters. I created two so I could specialize in ground combat and space and even took on different classes so that may be something you'll want to consider as well. My ground Klingon can take on space pvp pretty well so I can still jump back and forth between space and ground without nerfing myself.
Just random thoughts.
Very good idea mate. Since Klingon side is not fully developed be a good idea to get grasp of all that pvp will offer in the future. Ty.