When creating a new Security or Distribution group the entry will only be propagated to the Outlook Offline Address Book (OAB) at the operating system or application default sync times

Exchange regenerates the OAB – default generation schedule: 24 hours
Outlook downloads the OAB – default update schedule: 24 hours

So in a worse case it can take up to 48 hours before a user can see a new group in their address book

To Force Replication

On the Exchange Server run the Exchange Powershell script:-
Update-OfflineAddressBook -Identity "<name of the OAB>"

Example:

On the Client workstation in Outlook go to Send / Receive, Send/Receive Groups and select “Download Address Book”

References:

To change replication settings, check https://www.howto-outlook.com/howto/oabupdate.htm

https://docs.microsoft.com/en-us/powershell/module/exchange/email-addresses-and-address-books/Update-OfflineAddressBook?view=exchange-ps

https://social.technet.microsoft.com/Forums/office/en-US/bd3b7fd8-0e4c-415a-a990-b8575ab1ad89/how-to-push-to-update-offline-address-book-in-client-outlook?forum=exchangesvrclients