Growing old in a dream shows you are thinking about time: what remains, what matters to you, what you still want to experience? If it feels peaceful, you are at peace with your path; if it frightens you, something is pressing that you don't want to postpone.
Suddenly being very old can touch your awareness of time and impermanence. You may wonder whether you will experience or achieve certain things in time. The dream can also express a wish to approach a situation with greater experience and calm.