Because the ruling class of Westeros relies more heavily on control of military manpower than the ruling class of Essos, it’s usually the case that mercenaries in Westeros are usually Essosi free companies who’ve been brought over as additional troops and/or specialized troops (Myrish crossbowmen, for example), whereas native Westerosi largely serve in the armies of their liege lords.
However, there is a history of Westerosi mercenary companies being founded as a way to get inconvenient fighting men out of the country following a major political rupture:
- The Company of the Rose, for example, was founded by Northerners who refused to accept Torrhen Stark’s submission to Aegon the Conqueror, and preferred exile in Essos instead. Their departure for Essos meant that Torrhen wouldn’t have to deal with a large militant faction of nationalists, who might have supported his sons’ faction in Northern politics.
- The Stormbreakers were founded in the wake of the Dance of the Dragons, and likely absorbed a lot of the excess soldiers who had been mobilized during the Dance and now had no peacetime employment. Based on the name, I wouldn’t be surprised if the original founders were Riverlander veterans of the Battle of the Kingsroad, but I would also guess that no small amount of their number were made up of the surplus Northmen who were left behind after the “Hour of the Wolf.”
- The Second Sons predate the Conquest, which shows how long this tradition has been going on, and were formed more for economic reasons than political ones. As WOIAF tells us, the company was “founded by twoscore younger sons of noble houses who found themselves dispossessed and without prospects.”
It is important to note, though, that all of these free companies left Westeros and worked exclusively in Essos – which was probably quid-pro-quo for allowing them to be formed in the first place.