The state of being a Regency may be temporary; it is possible that, even with a Royal Heirs available, a King or Queen may appoint an Heir Designate to rule upon their Croaking. There may be restrictions upon this rule; a turn limit, the inability to name a new heir other than the living heirs, etc. It may be possible to name a Regent while an heir is still being produced.
Another possibility is that a side may be in the process of popping an Heir when the Royal is croaked, forcing the Chief Warlord to act as a Regent until the popping is complete. Considering the time and expense required to create an Heir, this is likely to happen.
A third possibility is that a non-Royal Overlord, perhaps a Noble, might conceivably adopt a Royal popped by another side as his Heir. By doing so, he might avoid much of the hostility that Overlords normally receive from Royals, and ensure that his side would eventually be able to pop more Royals and Nobles.
A fourth possibility is that it is simply a side ruled by an Overlord, but with Royals on it, granting access to some of the benefits of Royalty, such as the ability to pop Nobles.