For starters i'll just be happy to get some KDF PvE so I can use my awesome BO crew =D
But I hope there are no missons like the patrol you get from Sulu that takes you to Danteri system where you have to walk back and forth to solve a disbute between these 2 babies and scan some cargo and play mediator....
The Klingon version should be something like: You promptley and ceartively kill both disputers, take ALL the goods for the empire( and any cool stuff for you ) and take their women to be added to your personal play time group. Next system please >=)
Missions Klingon's have done in the Star Trek series.
Escort or Patrol missions
Space Monsters (V'ger anyone?)
Search and Destroy
Threaten a species
Search for more natural resources
Colony establishment including finding new habitable worlds to spread the empire to through colonies.
list can go on and on, each scenario can be based upon different episodes I've seen the Klingon partake in. This said PvE can be done with Klingon's.