According to the map images in The Valdemar Companion, Taymyrr is bordered in the north by Tolmassar, east by an unknown nation, west by Oris, southwest by a corner of the Empire of Holy Ithik, and primarily the southern border is shared with the tiny kingdom of Zoskin.
The capital city of Taymyrr is Stormhaven, and given the propensity for mercenary companies to name their base of operations with the suffix of "haven," it seems likely that Taymyrr may originally have been founded, an unknown period of time ago, by some mercenary company which was active in the vicinity. If this is the case, it is likely that the stated company became the official national army of the kingdom of Taymyrr, since Stormhaven is the capital.