Stars move through space all the time, they quietly rotate round the centres of galaxies, relatively slowly given the size of space but quite quick if you’re up close.
Assuming the star was a handy room temperature giant ball (instead of a massive hot ball of plasma), and you wanted to roll it away, you’d need to apply a lot energy to get it moving, momentum is mass times acceleration and stars have a LOT of mass. So it’d be possible, but you’d need a looot of energy and also for it to be in a state to handle it.
Well not really. The biggest source of gravity, the most massive thing will be the star itself. If there was no gravity the the star could not hold itself together, it would just drift apart ! The gravity is just part of what the star is so you cant separate one from the other.
Stars don’t stay at one place. All stars in universe are part of one or other galaxies. Stars travel around the center of their respective galaxies with a GREAT SPEED. If Stars and other celestial bodies would have stayed in one place, they would have fell on each other due to gravitational pull and eventually destroyed into a single point. Their motion helps them to create a balance against gravitational pull. Let’s take an example of our closest star Sun. It moves around center of our galaxy called Milky Way at a speed of 800000 Km per hour. Isn’t it a really high speed!!!!! Though, it takes 250-300 million years to complete one round because of the huge size of the galaxy. However, we don’t see such high speed of Sun, as we (earth, other planets and all other matters) are also moving along with Sun. Therefore our relative speed against Sun is negligible!!!!!!
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