Telemark has everything to offer a rifle or shotgun hunter. Reindeer, elk, red and roe. Add to that such oddities as beaver, capercaillie and blackgame and you could be ocupied almost year round. Ptarmigan and grouse can also be found, so there is no reason to stay gunless. What were you thinking..?
Where do you live, anyway? Most rural areas have a high density of hunters, and getting to know some will ease your way back in to hunting.
How to find hunting otherwise? Jff and your local shooting range has been mentioned already, but http://www.inatur.no" target="_blank is also a good option. Talk to anyone with farmland and ask if you can join them for the elk hunt if a space opens up. If you contribute to the skinning, gralloching and transportation of the deer, you will soon become a popular man. Besides, there is no reason not to travel outside Telemark
First step first: You need to get registered in the Norwegian registry of hunters and buy the "jegeravgift". If you have any hunting related qualification to show from the uk (Deer stalking certificate or similar), that will probably be sufficient as documentation. More info here: http://www.brreg.no/jeger" target="_blank. Call them and ask ho you can get registered.
Second: You need to use your registry as a hunter to apply for a firearms license. It is not nearly as strict as in the uk, and you'll get up to six long guns without much trouble as a registered hunter. Your local police will have the required application form. Processing time is is 2-8 weeks usually.
Third: Buy a gun and gun cabinet. Anything from 6,5x55 and up is legal for elk and everything else.
Fourth: You need to pass the hunter shooting proficiency test with every rifle you intend to use for big game every year. Two visits to the range required for a combined minimum of 30 practice rounds before the actual test: 5 shots on a deer target within a marked 30 cm circle at 100m. Your choice of position, but not support or bipod.
All legal and ready. Less complicated than it sounds! Welcome to Norway by the way. You'll like it here!