This year I took admission to the MTech program at IIEST Shibpur. Next year, can I use the same GATE score to transfer to an MTech at a better institute? If so, will my GATE scholarship be continued?

Yes, you can take admission even after two years in any other college or university as now GATE score is valid for 3 years. But few colleges keep the GATE scorecard until the course finishes. So if this is your case then you can leave or cancel the course and you will get your scorecard back. But when you take admission in any new college or university, you have to start again from 1st year. You cannot continue from where you left at your previous college.

Also, you should note that now adding an Aadhaar card to the GATE portal is mandatory so that they can track you if you qualify for GATE again and take admission with the new score.