Drive holding my database is running out of space. What are my options?
It depends on how your database is architectured (you do not say) and may also depend on the PostgreSQL version you are using (you do not say).

Anyway, in general, with PostgreSQL, you can create a new "tablespace" that is to make a specific new directory (so you choose the place, like on second drive) available to create new PostgreSQL objects, such as tables, in it.

See https://www.postgresql.org/docs/current/static/manage-ag-tablespaces.html that says Tables, indexes, and entire databases can be assigned to particular tablespaces. and gives this example:

CREATE TABLESPACE fastspace LOCATION '/ssd1/postgresql/data';
CREATE TABLE foo(i int) TABLESPACE space1;


Also, are you sure that the current content is really only data and not temporary stuff or useless indexes or just overblown tables because you are not running autovacuum or things like that (this depends a lot on which PostgreSQL version you run)?

If you have only a single table, with really 1950 GB of data in it, you will first need to partition it, in order to be able to move some of the content to a new tablespace (and/or archive some old content somewhere else).