Licensure follows the patient
The location that matters for telehealth is generally the patient’s, not yours. Sitting in one state and caring for a patient in New Hampshire generally means you need authority to practice in New Hampshire — via compact privilege or a New Hampshire license. See telehealth: patient in another state.
The law that governs this in New Hampshire
Caring for a patient located in New Hampshire is practice in New Hampshire, so it is New Hampshire’s own nurse practice act that defines what you may do and the New Hampshire Board of Nursing that applies it. That act is RSA 326-B (Nurse Practice Act); N.H. Admin. R. Nur 100–800.
The compact itself is separate law. New Hampshire adopted it at N.H. Rev. Stat. Ann. § 326-B:46 (Nurse Licensure Compact), which is what allows a multistate license issued elsewhere to reach New Hampshire at all — the practice act still decides what you may do once it does.
Compact status is not the only consideration
Even where a multistate license reaches New Hampshire, your employer and the New Hampshire Board of Nursing may impose additional requirements, and some roles carry their own rules. Compact status answers one question — it is not a blanket authorization to practice remotely.
APRN telehealth is separate
The compact covers RN and LPN/LVN licenses only. If you work as an APRN, your advanced-practice authority is granted state by state and is not carried by a multistate RN license — a point that catches out a lot of remote NP roles.
Since when has a compact license worked in New Hampshire?
Nurses holding another state’s multistate license have been able to practice in New Hampshire since January 19, 2018. It has been a member long enough that most guidance you find will be accurate on this point.