You can upgrade a Microsoft SQL Server Express instance using the SQL Server Express installation wizard.
The version of SQL Server Express delivered with ArcGIS has changed over time. The following lists the version of SQL Server Express delivered with each version of ArcGIS:
- ArcGIS 9.2: SQL Server 2005 Express Service Pack (SP) 2
- ArcGIS 9.3: SQL Server 2005 Express with Advanced Services
- ArcGIS 9.3.1 and 10: SQL Server 2008 SP1 Express with Advanced Services
- ArcGIS 10.1 through 10.2.2: SQL Server 2008 R2 Express with Advanced Services
- ArcGIS 10.3 through 10.4.1: SQL Server 2012 Express
- ArcGIS 10.5 through 10.6.1: SQL Server 2014 Express
If you created your database servers with ArcGIS 10.1 or a later release, you can upgrade your SQL Server Express instance when you install the current ArcGIS release using the SQL Server setup wizard provided with ArcGIS Desktop, ArcGIS Engine, or ArcGIS Server or ArcGIS Enterprise workgroup.
See Microsoft documentation for instructions on upgrading instances of SQL Server.
Once your SQL Server Express instance is upgraded, you will likely need to upgrade your existing geodatabases. See Upgrade a desktop geodatabase for instructions.