N.H. Rev. Stat. Ann. § 14-A:1

If the office of chairman of a committee of either branch of the general court becomes vacant for any reason at any time after the adjournment of the biennial session and before the dissolution of the general court under the constitution, the presiding officer of the branch of the general court in which the vacancy occurs may appoint a chairman to fill the vacancy from among any of the members of the committee in which the vacancy exists.