How do I skip a new ticket notification to a particular email address?

Yes, This can be done by creating a new Workflow Automator rule (Admin > Service Desk Productivity > Workflow Automator> New Automator) in Freshservice. Set the Event as Ticket is Created. In the condition block provide the condition as “From Email is” the particular email address and save the condition. Set the Action as Skip New Ticket Email Notifications.