Yes. Aging can cause the excess facial hair due to the drop in hormones. Actually, you may have always had the hairs, but they were much finer and not so noticeable before (hormones can also change the texture of the hair).

You may also have a small mole or kerotosis under or on the skin that can cause excess growth in a specific area. Check with your doctor or dermatologist. Hormone replacement for a few excess hairs seems a bit extreme. Your dermatologist will be able to determine if it is a skin growth, and if not, may be able to suggest something a little less drastic than hormone replacement.

It’s sort of true that as you get older you get more hair, but it’s hormone related. I’ll assume you are old enough to be going through menopause, then HRT will most likely halt any new growth. As for the current growth, you can probably get rid of it with laser (do it soon, before those hairs turn grey/white).