Rosemary is a very hardy, drought-tolerant and attractive perennial that thrives in Zones 8 to 10. It makes a beautiful hedge, growing as high as 6 feet tall. If your region is warm enough, consider transplanting your rosemary outside. It doesn't require very rich soil, nor is it especially vulnerable to pests, which makes it a good candidate for spending life in the great outdoors.
If a new container is in order, make sure it's big enough to accommodate the transplant for years to come: At least half again as wide as the plant and root ball, and deeper than the last pot. Rosemary doesn't transplant easily. Give it a fresh batch of rich, well-drained soil and take care to minimize shock by disturbing the roots as little as possible.
If the rosemary is an older plant, chances are good that even your best efforts at transplanting won't result in the best outcome; rosemary can be terribly finicky about being moved. But cuttings from the original plant should root fairly easily. Cut a section of new growth where the wood is soft and remove leaves that will be under soil. Dip the cut end in rooting compound and bury it at least an inch in depth into well-drained soil. Keep the cutting moist, but not wet. Once the roots are forming, this young seedling can be moved to bigger pot. Make several of these cuttings; you can never have too much of a good thing, anyway. If the older plant doesn't survive transplantation, your new seedlings will be able to replace it.