How long will tax lien be on my credit report in N.H.?

Any negative item will remain in your credit report for the next 7 years. As you've paid off the tax lien and it has passed 7 years, you should contact the credit bureaus and request them to take necessary steps in order to remove the tax lien from your credit report.

Tax liens remain in your CR until after 7 years from the date of payment. FCRA 605(a)(3). They are one of the few types of derogs where date of delinquency is not the controlling date.
If more than 7 years has expired from date of payment, the process is to file a complaint with the CRA under FCRA 605(a)(3) for their non-compliance. Dont label such a complaint as a dispute, or you will find yourself in the middle of a dispute process that is totally unnecessary and inappropriate. YOu are not contesting the accuracy of reporting of the lien, but rather the improper inclusion of it in your CR by the CRA.