“I Won’t Keep You” Means “I Won’t Take More of Your Time”

“I won’t keep you” is often used as a conversation is coming to an end. It does not mean “I won’t retain you”; it means “I won’t take up any more of your time”. Here, keep means to delay someone. The phrase respects the other person’s time while letting the conversation close naturally.

A: I’d better finish this report.
B: Of course. I won’t keep you.

You can also say, “Anyway, I won’t keep you,” when you want to bring the exchange to a close. It is usually a polite signal, not a claim that the other person is already impatient. “I won’t waste your time” can sound as though the conversation so far had no value. “I won’t keep you” is natural in Australian, British and American English; it is not uniquely Australian.

https://dictionary.cambridge.org/dictionary/english/keep
https://www.merriam-webster.com/dictionary/keep