We generally do not refer to a person's age when you want to emphasize how old someone is.
You may hear "My young friend" for an adult talking to a child, or an older adult talking to someone recently out of their teens, but we would simply not say "My old friend" to someone who is of advanced age.
If you want to REFER to that person to another person, you could say "My friend, who is a bit older,..." or "My friend, who is in her 80s,..." if the advanced age is relevant. (Like, you want to tell this other person a story they told you about the 1940s or something.)
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