Each state has its licensure board and process for social workers. That means they have different requirements. You cannot directly use a social worker license from another state in New Hampshire. The recourse is to apply for license reciprocity.
If you have been a social worker in a different state and transferring to New Hampshire, you do not have to go through the entire requirement and application process. The state acknowledges the fact that you already have the knowledge and experience to do the job. What you need to accomplish is to prove your previous licensure and applicable requirements.
For example, you do not need to retake the ASWB clinical exam to get a LICSW license in New Hampshire.
You need to submit similar requirements mentioned above, including all the documentation. Proof of your previous license needs to be included too. The application form is found in the regular application for the LICSW license.
The reciprocity process is aimed to help social workers continue practicing their profession in different states in case they need to move.