AIRAC cycle changes on Thursdays every 28 days (4 weeks), each country has a different time for when the new charts become effective. In the US the switchover time is 09:00Z.
Each airline will establish their own switchover policy, to ensure the charts are in effect, this procedure should be included in the airline's basic operations manual.
It is not possible (Boeing Pegasus FMS) to perform the switchover in the air, so in the case the AIRAC change will occur while in the air, best practice would be to takeoff with the old database active and perform the switchover after landing. Any STAR and/or IAP programmed into the FMS should (always) be verified with the appropriate effective chart (EFB or paper).
The reason the switchover cannot be performed in the air is because switching databases could clear the Routes (1 and 2) already programmed into the FMS.
An FMS CDU message of "Nav Data Out of Date" may be issued should the switchover not be performed in a timely fashion.
Again, this applies to Boeing FMS systems other manufacturers' procedures may differ.
Please consult with your training manager or chief pilot for airline specific policies. Don't be afraid to ask, it's better to ask a seemingly bad question than to remain confused.
Hint: Always check the aircraft clock (time/date) to ensure it is correct.