I am a MA salesperson who became licensed in NH last year. I'm not sure if process is same for broker but for salesperson I just had to apply for a NH license and take NH salesperson exam because NH has reciprocity with MA. You can find some information at
https://www.nh.gov/nhrec/ under the section exam information but it was still somewhat confusing what I had to do and in what order. I seem to recall I had to start application and/or contact the state before I could schedule the exam but I don't recall the exact order. I got confused about the order but the NH Real Estate Commission staff were very nice and helpful with the process. To maintain my NH license I will have to take continuing education in NH as well as MA for my MA license.