Depends. It would really help to know where you are and what your climate is like. But yes, you can plant in the same bed.
Carrots don't take up a lot of space. If you have a bed with tomato plants (for example) in it, while the tomato plants are still growing, you can plant a row of carrot seed down the outer edge of each long side of the bed, say in Aug, Sept or Oct. Eventually the tomato plants will be done and get out of the way, so for the fall/winter when the carrots need more sun, they won't be so shaded.
In late winter, you can do it the other way around. Plant carrot seed as soon as the ground can be worked, down the outer edge of beds. Then put your tomato plants in the middle once all danger of frost has passed, which might be six weeks later. Your carrots will be well sprouted by then. By the time the tomato plants are really big, the carrots can be harvested.
Carrots Love Tomatoes is the title of a book on companion planting!
So this is companion planting, not rotation. You do the rotation just by doing this whole thing again the following year, in a different bed.
Yes, some people (this means you, applestar,
) do very complicated three or five year rotation plans, but I don't.