To use the most modern version of Postgres software we need to add postgresql repository. Edit `/etc/apt/sources.list` or create `/etc/apt/sources.list.d/pgdg.list` and add there a line: `deb http://apt.postgresql.org/pub/repos/apt/ jessie-pgdg main`
Then import the repository signing key, and update the package lists:
```bash
wget --quiet -O - https://www.postgresql.org/media/keys/ACCC4CF8.asc | sudo apt-key add -
sudo apt-get update
```
Install a new version of PostgreSQL server.

Once the Debian upgrade finished, I used `dpkg-query -l postgresql*` to check which versions of postgres I have installed. 

```
dpkg-query -l postgresql*
Desired=Unknown/Install/Remove/Purge/Hold
| Status=Not/Inst/Conf-files/Unpacked/halF-conf/Half-inst/trig-aWait/Trig-pend
|/ Err?=(none)/Reinst-required (Status,Err: uppercase=bad)
||/ Name                        Version            Architecture       Description
+++-===========================-==================-==================-============================================================
ii  postgresql                  9.6+177.pgdg80+1   all                object-relational SQL database (supported version)
un  postgresql-7.4              <none>             <none>             (no description available)
un  postgresql-8.0              <none>             <none>             (no description available)
un  postgresql-9.1              <none>             <none>             (no description available)
ii  postgresql-9.4              9.4.9-0+deb8u1     amd64              object-relational SQL database, version 9.4 server
ii  postgresql-9.6              9.6.1-1.pgdg80+1   amd64              object-relational SQL database, version 9.6 server
un  postgresql-client           <none>             <none>             (no description available)
ii  postgresql-client-9.4       9.4.10-1.pgdg80+1  amd64              front-end programs for PostgreSQL 9.4
ii  postgresql-client-9.6       9.6.1-1.pgdg80+1   amd64              front-end programs for PostgreSQL 9.6
ii  postgresql-client-common    177.pgdg80+1       all                manager for multiple PostgreSQL client versions
ii  postgresql-common           177.pgdg80+1       all                PostgreSQL database-cluster manager
ii  postgresql-contrib-9.6      9.6.1-1.pgdg80+1   amd64              additional facilities for PostgreSQL
un  postgresql-doc              <none>             <none>             (no description available)
un  postgresql-doc-9.4          <none>             <none>             (no description available)
un  postgresql-doc-9.6          <none>             <none>             (no description available)
```

Looks like the Debian upgrade included PostgreSQL 9.6, but I still need to upgrade from 9.4 to 9.6.

Run `pg_lsclusters`, your 9.4 and 9.6 main clusters should be "online".

```
pg_lsclusters 
Ver Cluster Port Status Owner    Data directory               Log file
9.4 main    5432 online postgres /var/lib/postgresql/9.4/main /var/log/postgresql/postgresql-9.4-main.log
9.6 main    5433 online postgres /var/lib/postgresql/9.6/main /var/log/postgresql/postgresql-9.6-main.log
```

There already is a cluster "main" for 9.6 (since this is created by default on package installation).
This is done so that a fresh installation works out of the box without the need to create a cluster first,
but of course it clashes when you try to upgrade 9.4/main when 9.6/main also exists.
The recommended procedure is to remove the 9.6 cluster with `pg_dropcluster` and then upgrade with `pg_upgradecluster`.

Stop the 9.6 cluster and drop it.

```bash
sudo pg_dropcluster 9.6 main --stop
```

Upgrade the 9.4 cluster to the latest version.

```bash
sudo pg_upgradecluster 9.4 main
```

Your 9.4 cluster should now be "down".

```
pg_lsclusters 
Ver Cluster Port Status Owner    Data directory               Log file
9.4 main    5433 down   postgres /var/lib/postgresql/9.4/main /var/log/postgresql/postgresql-9.4-main.log
9.6 main    5432 online postgres /var/lib/postgresql/9.6/main /var/log/postgresql/postgresql-9.6-main.log
```

Check that the upgraded cluster works, then remove the 9.4 cluster.

```bash
sudo pg_dropcluster 9.4 main
```

After all you may totally remove version 9.4 from the server:
```bash
sudo apt-get --purge remove postgresql-client-9.4 postgresql-9.4
```
```bash
dpkg-query -l postgresql*
Desired=Unknown/Install/Remove/Purge/Hold
| Status=Not/Inst/Conf-files/Unpacked/halF-conf/Half-inst/trig-aWait/Trig-pend
|/ Err?=(none)/Reinst-required (Status,Err: uppercase=bad)
||/ Name                        Version            Architecture       Description
+++-===========================-==================-==================-============================================================
ii  postgresql                  9.6+177.pgdg80+1   all                object-relational SQL database (supported version)
un  postgresql-7.4              <none>             <none>             (no description available)
un  postgresql-8.0              <none>             <none>             (no description available)
un  postgresql-9.1              <none>             <none>             (no description available)
ii  postgresql-9.6              9.6.1-1.pgdg80+1   amd64              object-relational SQL database, version 9.6 server
un  postgresql-client           <none>             <none>             (no description available)
ii  postgresql-client-9.6       9.6.1-1.pgdg80+1   amd64              front-end programs for PostgreSQL 9.6
ii  postgresql-client-common    177.pgdg80+1       all                manager for multiple PostgreSQL client versions
ii  postgresql-common           177.pgdg80+1       all                PostgreSQL database-cluster manager
ii  postgresql-contrib-9.6      9.6.1-1.pgdg80+1   amd64              additional facilities for PostgreSQL
un  postgresql-doc              <none>             <none>             (no description available)
un  postgresql-doc-9.6          <none>             <none>             (no description available)
```