Depends on your goals. Unless you are amazingly fit and athletic, you are probably too old to become a professional dancer.

But if you want to pursue it as a serious hobby (i.e., not your source of income), you're NEVER too old! And you can start competing now if you want.

The big choice you need to make is whether you want to compete pro-am (with your instructor as your partner) or as an amateur (with another amateur as a partner). There are pros and cons to each; for most people, it depends on whether they can find an amateur partner and whether they can afford to compete pro-am (it's costly because you'll need to pay some or all of your instructor's expenses at the comp).

I started dancing when I was 50. I've done pro-am and started competing when I had been dancing only 6 months. Pro-am competitions are divided by both level and age. It varies depending on who's sponsoring the competition, but typically you can compete as a "newcomer" with less than 6 months or 50 hours of instruction. Then you progress up the levels, typically something like beginning broze, intermediate bronze, full bronze, beginning silver, etc. You also enter by your age level, so you'd be competing against other dancers more or less your own age. It is possible to enter as a newcomer in the over-80s age group! I often joke with my instructor that, having started at fifty, I have my eye on a national over-80s title--because it will take me that long to get that good! Amateur competitions call their dance levels by different names, but they too are geared for the dancer beginning as an adult.

Your instructor or the studio owner should be able to tell you more and whether your instructor or any others at the studio would be willing and able to compete pro-am with you.

Good luck!