You may know the song "THIS TIME AROUND" by Michael Jackson. Does it mean around this time, these days, or something like that?
'Around this time' and 'this time around' sound very similar but have quite different meanings.
'Around this time' - This is used when you are talking about an event that happened close to a particular period of time, or at nearly the same time as a particular event, e.g.
It's 9 o'clock. Bob usually drops in for a pint around this time.
'This time around' - This is used when a person is repeating an action or activity, and usually infers that this time they will be changing what they did, or how they behaved, during the previous occasion or occasions.
This is my third marriage; this time around I am going to focus on my marriage rather than my job.
This time around is an idiomatic expression in English.
If you go out (date) with someone for a period of time, then break up with the person, that was "a time" you were with that person.
Then, if you start going out with the person again, that is the second time you date them.
In colloquial language, if you started talking to that person about going out with them the second time, you can refer to that time as "this time around".
Please bear in mind, this is for a romantic situation. But the entire explanation could refer to any human situation in which something happens for a second time and you are referring to it. It could be a job, task, etc. where a thing happens for the second time.