How do you make an independent agency?

i dont know much about it. but like bounty hunter, how are they allowed to arest people without a badge? and private investigators? and i know this is a show but "human target" is realistic apparently. how can you make your own agency with only 5 people. and is it legal? Or most of these people dont get caught and the government isnt aware of there exist because they are proffessionals who use to be in cia or something?