New Hampshire does not provide special admission rules for government attorneys licensed in other jurisdictions.
However, New Hampshire provides a New Hampshire Multijurisdictional Practice Rule (MJP) within its rules of professional conduct. Comment 16 to that rule provides for an interpretation that exempts government attorneys from the unauthorized practice of law.
Please also see the New Hampshire Bar Reciprocity page to view the requirements for Admission on Motion, and the New Hampshire Pro Hac Vice page to view the requirements for admission to a particular proceeding.