Should a character's second-in-command advance? If so, how?

One of the characters in a game I run has a romantic relationship with an NPC of minor importance. She’s the second-in-command of his smuggling organization and a bit of a thug. I gave her a full burn before we started playing. Should I advance her as we play or leave her as she is? If I should advance her, should I advance her naturally, making tests for her and marking advancement, or should I just eyeball it, and loosely increase her capacity for the stuff we see her doing?

Since you’re using Roll20, I’d say just use tests + advancement because it is easy to track using the sheet.
When you’re giving an NPC a full burn, then I assume that includes most of the mechanics used by players, and nothing as written says they cannot advance.

In my game, my major NPCs aren’t exactly advancing because it’s only been two sessions and they don’t get as much screen time as the PCs. However, I do give them BITs and allow them to earn Artha at the end of the session the same way as players just to give them more of an edge (considering the current major NPC is a pseudo villain).

It’s tricky! The NPCs should definitely grow as they trudge along their PC companions, but I don’t think tracking advancement as a PC would is necessarily the best way to do it. Maybe once a campaign… or trait vote?.. give them a boost in stats and skills. Or to be more official, use the Practice rules for them and reconfigure them at a regular basis.

Not sure if I’d mark tests, because I’m lazy, but if the player wanted their second-in-command to advance, as the GM I’d let them come up with the NPC’s practice during down time.

Less paperwork for me, a better follower for them.