You need to verify that your on-premises SSAS server supports the same or higher compatibility level as the AAS model (1500 in this case). SQL Server 2019 and 2022 support compatibility level 1500.
Use the Tabular Model Scripting Language (TMSL) or SSMS to export the AAS model metadata as a JSON or .bim
file.
You can also use SSDT or Visual Studio with the Analysis Services projects extension to open the exported .bim
file.
Then update the connection strings and data source configurations if required (if your data sources are also moving on-premises) then deploy the model to the on-premises SSAS instance.
https://learn.microsoft.com/en-us/sql/ssdt/download-sql-server-data-tools-ssdt?view=sql-server-ver16