Short answer: yes, you could get the entire tattoo removed, but it would be a long, expensive and painful process, as that is quite a large tattoo!
Long answer: Your tattoo actually looks beautiful, and was very well done. Yes, you can still see the star, but cover-ups are difficult, and the artist has to work with what they're given. What I would suggest, rather than removing a very nice tattoo is going back to the artist and asking them to make parts of your tattoo a bit darker so that the star will be less noticeable. For instance, the green and blue parts of the swirls could be made darker so that the lines of the star blend in more. Talk to your artist -- a good one will do whatever it takes to make you happy with your piece, but also remember that sometimes a tattoo cannot be completely covered, especially if the outline is black.
Hope this helps!