The question is rather broad. A lot of information is missing, eg are there any cross-database queries, what type of processing is performed, how big is the database? Are all databases on the same server?
There are a lot of options:
It sounds like this database is reference data from a government application. In which case, one can just copy it to another database with a well-known name.
Rigerta Demiri already posted how you can execute queries against the latest database if you don't run cross-database queries, ie if you don't want to join data between your database and the application's. Just change the target database. You can do that in the connection string too.
You can also just copy the data from the latest database into your own, with an SSIS package. The source (ie the reference database) can be modified programmatically. It can also be specified as a package parameter.
You can create SYNONYMs in your database for the reference tables with CREATE SYNONYM MyTable FOR ThatDB.dbo.MyTable
. This can be automated with a script that reads the latest database name, drops the old synonyms and creates new ones with the latest database.
Which is best depends on the data volume, type of data, how often it changes, how it is used, how much time you are willing to spend on maintenance etc
UPDATE
I forgot a more advanced scenario - if the data does change, read only the modified rows from the source database and copy them to the target. In other words, treat it just like any other ETL scenario. SQL Server offers lightweight change tracking since 2005, which has to be activated per-table. If you don't want to modify the source each time a new version is deployed, you'll have to drop back to checkiing timestamps or created/updated fields.