For renewals, vehicle inspections are done once a year during your renewal month (which is usually your birth month unless the vehicle is leased or in a business name).
There is a ten-day grace period into the month following expiration for inspection only– not for registration. For a new registration with new plates (or transferred plates) inspection must be completed within 10 days following registration.
An inspection sticker is valid as long as the vehicle is registered, but cannot be issued for more than 16 months.
Inspections can be done 4 months prior to the expiration date and will be valid to the following year.
More information on RSA 266:1 State Inspections.