PvP's been covered above, but if you're looking for PvE alternatives, a couple of suggestions.
CZs are what you mentioned. Instances like RES sites, or CNBs are sort of the same, but no faction or side is joined, you're just identifying and engaging wanted ships. There's no win condition, just sort of freelancing. If you find the intensity of this sort of combat doesn't provide enough challenge then the pirate threat instances are a big step up. Nothing in my Elite career came as as a big of a shock as my first visit in a pirate threat. I felt just like the soldier, Bors, in Monty Python's Holy Grail who said the immortal words
Right! Silly little bleeder. One rabbit stew comin' right up!
Then I nearly lost my ship against a freakin' NPC Chieftain. That thing was no joke, and no mistake!
I warned you, but did you listen to me? Oh, no, you knew it all, didn't you? Oh, it's just a harmless little bunny, isn't it? Well, it's always the same. I always tell them....
Assassinations are another good PvE option. AX combat (NHSS) is a different sort of challenge, though I've only done scout hunting. But it encourages a different sort of build, unique weaponry and outfitting, and targets that have skills and advantages that NPC ships don't have. A nice change of pace.