"The" seems more natural for this context, and the article I would choose, but they are actually both correct. "The female equivalent" -- suggests that there is only one female equivalent of "Sir" "A female equivalent" -- suggests that there may be more than one female equivalent of "Sir" Actually, your second sentence ( a female equivalent) sounds really bad. Let me illustrate the difference that you get from using different articles with the help of the following examples: Please name the female equivalent of "sir".
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.