ILO, I belive you're confused by the definition of government, and understandably so. There are two words we shouild use when discussing thsit topic. "Government," which means an organizational structure of society, including institutions, justice system, security services, and so on; and "state," which is a type of government that uses force to survive. In an Anarcho-Capitalist society, there would be a government because there would be a structure of insitutions that serve to organize society, such as dispute resolution organizationss, securityu companies, notaries, whatever. So, yes it's possible to have a government without violating the NAP, but is it not possible to have a state that does not violate the NAP, because a state, by definition, must forcefully assert authority to resolve disputes in a certain geographical area, and most of the time also steal wealth from the people.