Through various events, my PKs will shortly find themselves taking command of the garrison of a small motte and bailey castle. It's not theirs, but belongs to their liege lord. It is kept manned because it is close to the lands of a rival baron.

I know the castle needs at least 10 professional soldiers (I'm assuming a typical mix of knights and footmen). What I'm wondering is what other staff it should have. Would it be expected to have a full complement of officers, courtiers and servants as if it were an Estate of appropriate size? Or would it have a smaller staff, perhaps only the soldiers themselves with a handful of servants?

So one of the PKs is the castellan? Such would be the normal procedure.
As for other staff: that is up to you as the commander in chief here. It is possible that the liege lord of the PKs has installed a staff there already and it needs no more. So in such a case there would be, more or less, a permanent staff at the castle--a cook, a priest, etc
Alternately, maybe the castellan brings in his own staff and replaces the old one, who would have been temporary if this scenario was to occur.
But I urge you to make one of them castellan, while the other are his trusted circle of friends.

So one of the PKs is the castellan? Such would be the normal procedure.
As for other staff: that is up to you as the commander in chief here. It is possible that the liege lord of the PKs has installed a staff there already and it needs no more. So in such a case there would be, more or less, a permanent staff at the castle--a cook, a priest, etc
Alternately, maybe the castellan brings in his own staff and replaces the old one, who would have been temporary if this scenario was to occur.
But I urge you to make one of them castellan, while the other are his trusted circle of friends.

Yes, sorry. I'm never sure if I'm over-explaining or under-explaining. One of the PKs has been named castellan while the others are his trusted circle of friends who he is taking with him to form the core of garrison (except of the one Player Lady who is going to have find some way to sneak off to join them on adventure, but that's a whole other story).

The former castellan has been promoted to marshal to replace a fellow who died in battle and the on PK is being given this office as reward for his heroic deeds and as a chance to prove himself as a leader of men. I've been envisioning some roleplaying opportunities as the new knights deal with an existing staff left behind by the old castellan. I may leave it to them to decide whether to bring their own staff or keep the existing staff, or some mix of the two.

In most cases, the castle will have associated lands (especially in the earlier periods). The constable (castellan) would be granted control of these lands while in office to support the garrison (and maintain a higher standard of living as an officer of the lord). Some staff might be 'permanent' but the constable would likely transfer his household to the castle unless it was considered a particularly dangerous or temporary position.

In the earlier periods, many knights will owe Castle Guard duties. Thus you might have a new group of knights serving in the garrison every few months (say quarterly or something). If you have some rivalries among the liege's knights, you could create some conflict and intrigue using these knights. It could be as simple as feuds breaking out over who gets what living quarters and seating at the table. For example, if the castle has towers, vassal knights might expect to be given private accommodations in a tower and to be allowed to fly their banner from that tower (There is a painting/drawing or Richmond castle with each tower occupied by a different knight on Castle Guard). If a non-PK does get accommodations suitable to his station, he might work to undermine the constable etc.

Theoretically you could also cycle the other PKs through, so that the constable has periods with supporters and without supporters. That does create some group dynamics problems, obviously.

Would it be expected to have a full complement of officers, courtiers and servants as if it were an Estate of appropriate size? Or would it have a smaller staff, perhaps only the soldiers themselves with a handful of servants?

We are looking at something like 3 knights and 9 footsoldiers, so three manor's worth? Yeah, sure, I'd treat that as a £30 estate as far as the staff is concerned. If it is suddenly reinforced to like 10 knights and 30 footsoldiers, it wouldn't suddenly get boosted to a £100 estate, though, although a couple of the knights might bring some extra servants with them.

I might start skimming away courtiers and such, though, as they would be more likely to be back at the liege, but this is such a minor detail that it would be very unlikely to even come up in our campaign.

The £30 might support a basic garrison (as noted) with additional knights from Castle Guard.

NT