If you can do something any time or at any time, you can do it whenever you want to.
If you'd like to give it a try, just come any time.
They can leave at any time.
When you use any time without ‘at’, you can spell it anytime.
I could have left anytime.
We'll be hearing from him anytime now.
If you want to say that something can be done whenever a particular thing is needed, you can use any time with a that-clause, usually without ‘that’.
Any time you need him, let me know.
Any time the banks need to increase rates on loans they are passed on very quickly.
Any time is also used in negative sentences to mean ‘some time’.
We mustn't waste any time in Athens.
I haven't had any time to learn how to use it properly.
When you use any time to mean ‘some time’, you do not spell it ‘anytime’.