I'm not familiar with Persona 5, but...
Two ways include using a timer (behavior), or an incrementing counter variable.
I'd say a timer might be better suited to having time pass in real time, and a counter variable would be better for a action based/trigger type system. Of course you can use both together too.
You would have two variables, to keep track of days, and time within the days.
Lets say your incrementing counter variable represents hours. Every time you take an action (that takes one hour), add one to that variable. When the variable reaches 24 (or 16 or however long your "day" is), reset it to 0, and trigger a new day (add one to your "day" counter variable).
If you wanted in real time, you can do something similar. Lets say 5 minutes represents one hour. Use the timer behavior, set it for 300 seconds, and when the On Timer condition triggers, add one to the "hour" variable.
You can break it up into minutes if you wanted to, the concept is the same. When you have variables keeping track of your game time, you can use conditions to compare those variables to values you want to trigger or activate during specific times in game.