The line is said by the principal who was once a coach of a baseball team, then I think it's just "na" not "nasai"

My classical Japanese scholar husband says that in common speech it`s mistaken for the regular "な", but following て is derived from なさん, an older form of なさい.

Whether it is correct in modern context, I can`t say, but everyone around me agrees that as a confirmation な (like with ね) it sounds unnatural. Especially coming from a えらい character.

That means the same as 離れてね and 離れたんだ

Old men or people in a high position occationally use な　like that almost only in literary works, TV dramas, and so on. We usually don't use it in the real world.:)

What the principal ment is that 野球を離れて、今は校長だ。
Certainly, 離れてな is possible as a shortened form of 離れてなさい. But it in the case is different on intonation from a shortened form of 離れてなさい. We have to distinguish them by intonation and contexts.

What Debezo said was correct.

Oh, I cant learn this from anywhere , haha, Ty