William just told me that they've finally released the official PK 1.3 version. This means that you'll have to replace your current beta 1.3 version with this. Delete your old Persistent Kingdoms folder and put the new folder in. Remember that it's the subfolder called "Persistent Kingdoms" you want in your modules folder, not the folder called "Persistent_Kingdoms_1.3".
If this is the first time you're downloading Persistent Kingdoms, simply find the folder called Persistent Kingdoms inside Persistent_Kingdoms_1.3.rar and put the Persistent Kingdoms folder in your Modules folder. If you do not know where this is located, it is usually in either:
C:\Program Files (x86)\Steam\steamapps\common\MountBlade Warband\Modules or C:\Program Files (x86)\MountBlade Warband\Modules