What you probably want to do is add the PostGIS functionality to the existing database. The one with no function probably doesn't have the PostGIS at all.
if you've got PostgreSQL 9.1+, you can run the following command on the database missing the functions:
CREATE EXTENSION postgis;
This will add all PostGIS functionality to the existing database.
If you are running a lower version of PostgreSQL, there are a few more steps to undertake to import all the functions.
I'll refer to the official documentation for those steps: http://postgis.net/docs/postgis_installation.html#create_new_db
A blatant copy/paste in case the link dies:
Many of the PostGIS functions are written in the PL/pgSQL procedural
language. As such, the next step to create a PostGIS database is to
enable the PL/pgSQL language in your new database. This is accomplish
by the command below command. For PostgreSQL 8.4+, this is generally
createlang plpgsql [yourdatabase]
Now load the PostGIS object and function definitions into your
database by loading the postgis.sql definitions file (located in
[prefix]/share/contrib as specified during the configuration step).
psql -d [yourdatabase] -f postgis.sql
For a complete set of EPSG coordinate system definition identifiers,
you can also load the spatial_ref_sys.sql definitions file and
populate the spatial_ref_sys table. This will permit you to perform
ST_Transform() operations on geometries.
psql -d [yourdatabase] -f spatial_ref_sys.sql
If you wish to add comments to the PostGIS functions, the final step
is to load the postgis_comments.sql into your spatial database. The
comments can be viewed by simply typing \dd [function_name] from a
psql terminal window.
psql -d [yourdatabase] -f postgis_comments.sql
Install raster support
psql -d [yourdatabase] -f rtpostgis.sql
Install raster support comments. This will provide quick help info for
each raster function using psql or PgAdmin or any other PostgreSQL
tool that can show function comments
psql -d [yourdatabase] -f raster_comments.sql
Install topology support
psql -d [yourdatabase] -f topology/topology.sql
Install topology support comments. This will provide quick help info
for each topology function / type using psql or PgAdmin or any other
PostgreSQL tool that can show function comments
psql -d [yourdatabase] -f topology/topology_comments.sql
If you plan to restore an old backup from prior versions in this new
psql -d [yourdatabase] -f legacy.sql