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Yes.
While spousal support is waived if it's not sought during a divorce, child support doesn't work like that. Child support cannot be waived, as that would be contrary to public policy. Even if a parent hasn't previously sought child support, a parent may do so at any time.
New Hampshire's Division of Child Support Services can assist a parent directly with establishing a child support order and, after the order is established, with enforcing the order. DCSS charges only $25 per year, and that sum is not charged until at least $500 in support has been collected from the other parent. Further, that sum is not charged if a Custodial Parent is receiving public assistance.

New Hampshire's Division of Child Support Services
http://www.dhhs.nh.gov/dcss/index.htm

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