adding more space to the existing 9.6 cluster

Hello, we are almost out of space on our main data directory, and about to introduce new directory to our cluster. We cannot use multiple physical disks as a single volume, so we are thinking about creation new tablespace.
Our current data_directory shows as follows:
/data/postgresql/9.6/main
postgres=# SELECT spcname FROM pg_tablespace;
spcname
------------
pg_default
pg_global
(2 rows)

We also have 36 existing databases on this cluster.
If we add new directory, will it be enough to execute the following commands in order to force new data there:

CREATE TABLESPACE tablespace01 LOCATION '/data/postgresql/9.6/main01';

ALTER DATABASE db_name SET TABLESPACE

tablespace01

Do I need to repeat it for all our existing databases? Should I change our "template*" dbs as well?
Do I need to do something else?

Thank you for your advises.

-Julie