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Teams do not recieve New Ticket alerts. The only people who can receive New Ticket alerts are the Admin Email, Department Manager, Department Members, and/or Organization Account Manager. Teams will however receive the Ticket Assignment Alerts. To receive these make sure you have the Ticket Assignment alert enabled and configured for the "Team Members".

Then in the Team settings make sure "Assignment Alert" is unchecked.

Then in the Team settings click the Members tab and ensure Alerts is checked for all Agents.
Cheers.