All migrants must meet health and character requirements. There will be detailed questions asked about your background and you will be required to provide police certificates from any country you have lived in for over 12 months in the last 10 years (if you are the first-time resident visa applicant) or for over five years since you attain the age of 17 years if you apply for a temporary entry visa.
In terms of the answer, there are three things: character requirements for residency, a national security check (NSC) and the reputational side. In terms of the character requirements, if you have had no convictions, no deportations and no character issues, all that would be required in a police clearance from the country of citizenship and any other country you lived in for 12 months or more for the last 10 years. As for the NSC, this is more about information, i.e., because of the nationality, and completing additional forms etc., and waiting, as this is a long process. As far as I am aware, there is no ban on Iranian nationals. This leads us to the reputational, i.e., public security, public order or public interest, and the "fit and proper" person requirements. This could be something that the officer looks at for an Iranian applicant, especially if he has been tied up with regime in Iran or government and so on. Therefore, while possible to apply, there is no guarantee of success.
There are two main parts to background checks. Applicants age 17 and older are required to provide police clearance certificates with the residency application. These are obtained from their country of citizenship and any country where they have lived for 12 months or more (cumulative) in the last 10 years. Immigration NZ will also conduct its own background checks, a process that will usually take three to six months but can be longer. The purpose of these checks are to find good character from applicants and ensure they do not pose a security risk. You are not discriminated against by your nationality, so you don't need to be concerned about U.S. sanctions based on nationality.