Hi,
There is no downtime. After you purchase reservation for the number of vCores you need, the discount for compute will be applied automatically.
NOTE: The above assumes you are currently running Azure SQL Database vCore Provisioned.
To purchase reservation you may navigate to Reservations in the Azure portal:
When making your purchase you want to make sure you select the correct Performance Tier, Region, Term (1 or 3 years), Billing Frequency, and quantity. Performance Tier, Region, Quantity need to cover the Azure SQL resources you are currently running.
Please see article below for more information:
Save on compute costs with Azure Reservations - Azure SQL Database & SQL Managed Instance
Additionally, I recommend you review Azure SQL Database Reserved Capacity FAQs at the bottom of pricing page:
https://azure.microsoft.com/en-us/pricing/details/azure-sql-database/single/
Please click Accept Answer and upvote if the above was helpful.
Thanks.
-TP