My current drain pipe for the bathtub is left, however, I bought a tub with center drain. Is it possible to get to the left drain without replumbing?

No. You can use the old drain, but you will need to add a trap directly under new tub waste and overflow then pipe over to the existing drain and vent. This may require drilling some joist, or if on a slab, breaking up concrete and replumibing. Good luck and please let us know how things work out.