The Session State Service Application cannot be created from the Central Administration. For doing so, we have to do it through powershell. Here are the commands to create the database, the proxy service application and the service application.
Open powershell with administrator rights and type:
$serviceApp = New-SPStateServiceApplication -Name "StateServiceApplication" New-SPStateServiceDatabase -Name "StateService_DB" -ServiceApplication $serviceApp New-SPStateServiceApplicationProxy -Name "StateServiceApplicationProxy" -ServiceApplication $serviceApp –DefaultProxyGroup
After that you should see the service application and its application proxy in the Central Admin UI.
Hope it helps!