You can do this by editing the XML Files

I am not familiar with this mod, but in general, you can edit Civilopedia entries of units following these steps:

1. Find the unit's declaration and get the name of its Civilopedia tag. The unit's declaration is usually found in the CIV4UnitInfos.xml file which is in the folder Assets/XML/Units. Within this declaration you will find the Civilopedia Tag and within it the unit's Tag for the Civilopedia. If this is empty you should fill it, preferably using the naming scheme used by the other entries. If this unit declaration does not exist, it means this unit is not in the game at all and therefore doesn't appear in the civilopedia.

As an example, here is the declaration of the Archer:

<UnitInfo>
    <Class>UNITCLASS_ARCHER</Class>
    <Type>UNIT_ARCHER</Type>
    [...]
    <Civilopedia>TXT_KEY_UNIT_ARCHER_PEDIA</Civilopedia>
    [...]
</UnitInfo>

2. Search for the unit's Civilopedia entry. Using this tag, you can look around if there is an existing Civilopedia entry. It will probably be in the file CIV4GameText_Civilopedia_Units.xml in the folder Assets/XML/Text. Note that this doesn't determine if the unit appears in the Civilopedia, this just controls the description text there for it.

Here is the entry for the Archer:

<TEXT>
    <Tag>TXT_KEY_UNIT_ARCHER_PEDIA</Tag>
    <English>[TAB]The bow and arrow, invented in prehistoric times, greatly improved the hunting skills of early man, allowing him to kill his targets from a distance. [...]</English>
    [...]
</TEXT>

It might be that the Civilopedia entry for your specific unit is not showing because there is a typo or some other minor mistake within one of these steps. However if you cannot find any Civilopedia entry at all the unit's XML declaration is either missing completely, or the creators of this mod specifically declared this unit in a way, that disables it from being shown in the Civilopedia.

Make sure you edit these values at the right place

The above is an example of editing the base values of archer. In order to edit these for a mod, you would first have to find the mod's folder. It's typically under your game's base folder and then mods. If you play one of the expansions pack, you need to first go into the Beyond the Sword or Warlords subfolders and then in the mods folder's inside of those.

Note that not all mods have all of the files and folders of the base game in them. They typically only have the ones they are actually changing and the game knows that it must use its regular assets for the files that are missing in the mod. I would assume your mod should have its own copies of both files mentioned. If not just copy those files from the game's base Assets folder into the mod folder using the same folder structure and then edit them there.

In your case the developers probably disabled that unit's entry

If the Azer is a unit in the mod, but not shown in the Civilopedia, that is an odd case, that I haven't encountered before. My guess would be, that it has something to do with the categories, that this unit is classed into in the wiki: "Units without a Unit Class", "Unbuildable Units" and "Event Units". One of these probably makes it so, the unit is not appearing in the Civilopedia.

To know for certain we would have to take a look at its XML declaration and compare it with a unit from the base game or another unit in the mod, that appears in the civilopedia and see if there are any important differences or missing values.