Let us discuss what we know, from ER3145 and TRO, the state of the merc market, potential benefits and potential problems with major employers.
Federated Suns- Definately hiring, but good luck buying replacement equipment off the Quartermaster IMO. IMO, I think they will be hiring a lot of raiding companies for the Drac and Cappie fronts to help guerilla units. Travel behind the lines, strike at detachments, supplies and materials, then leave.
Lyran Commonwealth- Depends on how much the fall of the ELH is general knowledge. All of those merc commands died on Hesperus while the regulars left them as fodder. Generally the biggest nightmare to mercs afaik. Again, I am not sure you will be able to purchase replacement gear with the state of the LCAF. Oh yeah, typical posting location would be the Falcon front against Mad Malvina? Fun
Draconis Combine- Death of the Nova Cats could be a cause for concern . . . but they have Wolf's Dragoons and are pounding away at the FS.
Capellan Confederation/MoC- Might militarily be in the strongest position though it will depend on how they digest the conquest. Also have to see how much material and perhaps units they draw from the Canopus and Andurien, sort of the new Trinity. Might have problems with Andurien since they took worlds- kindling the old rivalry.
Free Worlds League- Reborn, I am not sure they were using that many mercs to do the fighting that ensued. Definately at odds with the Republic Remnant, the Regulans have an interior position and they should have an uneasy peace with the Wolf Empire. On the other hand, Lyrans are easy pickings so perhaps they can reverse some of the Hammerfall/Wolf losses by picking at the border.
Duchy of Andurien/MoC- Most junior member of the CC/MoC/DoA Trinity. Lost worlds to Jessica when the dump blew. Gave worlds to the Cappies to make it stop. Regulans are allies, but how useful are they when they did not help against Oriente? Will Ilsa send units into the Duchy to face the FWL or will she be giving them to Daoshen to use?
Regulan Fiefs- Surrounded by enemies, might be taking more of the independent worlds between them and Andurien so they have an 'out' astrographically. Only allies have fallen under CC/MoC control . . . would they really be hiring?
Republic Remnant- Sure they have needs, but do they have coin? Can they even resupply anyone? Do you expect the Fortress to come down?