Units earn experience points and can be upgraded. This guide on How To Upgrade Troops In Mount & Blade II Bannerlord explains how you can improve units that are in your party, once they have gained enough experience to reach the appropriate mark to upgrade.
Whenever you recruit troops at towns and villages, not Companions, they arrive as a tiered unit. Typically they are normally Tier 1, the weakest of troops in that particular troop group. For example, Imperial Recruits are Tier 1 units but once they have the required experience points, they can be upgraded to Tier 2. The second Tier for Imperial units can either be Imperial Infantryman or Imperial Archers. Most of the different units in the game follow the same tiered progression path.
How To Upgrade Troops In Mount & Blade II BannerlordEach battle your units earn Experience Points. You can see on the Battle Summary screen that sometimes your units will get Upgrades. This doesn’t actually upgrade the unit instantly, it’s a notification to tell you that a unit can be upgraded.
Open the Party screen and select a group of units. You should see an icon showing that they can be upgraded. Expand the troop unit and you will see the icons below, showing what paths are open to that particular troop unit. Simply select the unit and them select the unit upgrade you want to apply. It does cost some cash each time but it’s not very expensive in the earlier levels – and it’s much cheaper to upgrade your own than buy the more expensive versions of the same unit.