Everyone needs some form of border guards, and they're usually at least paramilitary if not a full-up branch of an armed force. With all the world-conquering going on during the Succession Wars it only makes sense for most Houses to have had some form of dedicated garrison forces, which would not need to be Mech-heavy because they're hopefully fighting "only" insurgents and guerrillas. A mixed force of AeroSpace and Military Police w/ a dusting of Light 'Mechs and Vehicles would probably do the trick, be fairly easy to move around, and free up your assault troops to move on to the next target.
In the canon novels (such as those about the Fourth War) this role is filled with troops under the generic name "militia" but it's unclear what is really meant by this term. Generally "militia" in the novels (and sourcebooks) rolls over and dies in front of "real troops", implying they're not equipped with 'mechs. But the Third Battalion of the Kathil Militia (the only one not mobilised and sent out on this duty in 3029) nevertheless was a 'mech formation, fielding homogenous lances of light 'mechs (Urbanmechs, Javelins, and something else which slips my mind).
For my personal BT AU, some of the Great Houses field Gendarmerie regiments (such as the FedSuns Outback Rovers, a brigade of 7 light 'mech formations built on the lines of March Militia RCTs, but with only one armor regiment and a full regiment of Engineers; they tend to operate in battalion-sized units similar to the Ceti Hussars but specialize in Civil Affairs and anti-Piracy in the FedSuns Outback). The Duchy of Andurien, meanwhile, field both reinforced MP units (the Carabinieri) and anti-piracy pure-areospace wings (the Andurien Borderers); the former officially falls under the Ministry of the Interior while the latter falls under the joint authority of the Ministry of Transportation and Ministry of the Exchequer.