As of this date, I would suggest upgrading to PostgreSQL-15. You can follow the official upgrade documentation: PostgreSQL: Documentation: 15: 19.6. Upgrading a PostgreSQL Cluster process.
The fastest upgrade option is using Upgrading Data via pg_upgrade and the --link flag which creates hard links to the files on the old version cluster so you don’t need to copy data.
Before selecting any upgrade method please consider below as mentioned in PostgreSQL upgrade document:
For major releases of PostgreSQL, the internal data storage format is subject to change, thus complicating upgrades. The traditional method for moving data to a new major version is to dump and restore the database, though this can be slow. A faster method is pg_upgrade. Replication methods are also available
For such cases, Testing upgrades in Pre-prod is recommended before the Production upgrade.