N.H. Rev. Stat. Ann. § 261:96

If any number plate supplied by the department is lost or mutilated, or if the registration number thereon becomes illegible, the owner or person in control of the vehicle for which said plate was furnished shall apply in writing to the department for a new plate and deposit with his application the proper fee; and thereupon the department shall issue to such applicant a permit allowing him to place a temporary plate bearing his registration number upon said vehicle until a plate of the regular design is made and delivered to him.