What should I do with this large database filling up the disk?
You have a few options. However, if your database is this size, normally it would only grow.

First option, make sure you need all the data. Ask to the business if it is necessary to keep all data, if not you could write some kind of archiving process to clean up older data, making place for new data to come in.

If your SQL Server version is enterprise you could benefit greatly by implementing row compression or even page compression, this will definitely compress your tables. However before you implement this always test, because this can have a negative effect on your performance. Especially when using Page compression. If your bottleneck is CPU I would not implement it. Here is a blog on what benefits you can get. 
https://www.mssqltips.com/sqlservertip/3187/demonstrating-the-effects-of-using-data-compression-in-sql-server/

Another thing you can do is add another disk to your database and add an additional filegroup &amp; files on that disk. Then rebuild your indexes to that filegroup, in that way you open up space inside your current files, and you can use 2 disks instead of 1 for your data storage. This will also in most cases improve your IO operations. https://www.mssqltips.com/sqlservertip/2601/using-multiple-filegroups-for-a-database-and-changing-the-default-filegroup/

If you have partitioning in place, you could store parts of tables on other disks as well. This will also make the maintenance of your indexes easier since you can rebuild a partition instead of a whole index.

Also if this is a datawarehouse database, I've seen epic datacompression using Clustered Columnstore Index on your Fact Tables.

That are the thing I would look into.