I assume you are refering to low level pvp. And no there really isn't any. As you get higher level, you will slowly start to find some here and there. Until then, I'd recommend you grind a little off the "exploration" cluster areas that your given. You can also do, for a near guarenteed 1x level boost, the Empire Defense against <race> Mission. At least that will help you level up to max level while waiting for PVP Queues.
I miss what the PVP was like when the game was first released. Back then you could eaisly level a Klingon solely on PVP.. But those days are long gone. So do the best you can.