First mentioned in the Assassins' Guild Diary, Miss Alice Band is a younger member of the teaching faculty at the Assassins' School, employed to expand the female teachership at a time when Guild membership was becoming more genuinely co-educational and new Houses (Scorpion House, Raven House, Black Widow House, and Tump House) were being established to absorb an influx of female pupils. In fact, she is House Mistress of Tump House, and therefore stands in loco parentis to her pupils, over and above being teacher to them. She teaches Traps, Locks and Climbing at the Guild, and is also a "stealth archaeologist". In Night Watch she sent trainee assassin Jocasta Wiggs on a very humbling training mission to target Sam Vimes after deciding that Ms Wiggs was an overconfident pupil.
Her first speaking part in the canon occurs in The Minutes of the Meeting To Form The Proposed Ankh-Morpork Federation of Scouts. (This is a short piece published in A Blink of the Screen. In this we learn that Miss Band is part of a select group called together to establish, sponsor and give practical guidance to Scouting. She is the Assassins' Guild representative on this project, and gives her opinion that young student Assassins are already pretty much up to speed in many of the desired skills and character attributes. Lord Vetinari observed that he would be grateful if certain Assassin skills were toned down somewhat while in the scout hut, as the underlying intention is to steer young people away from lethal weaponry. Miss Band is also wholly in favour of Scouting being inclusive of girls, who may well need a different sort of Guidance.
It is possible that she might have had a larger part to play in the Discworld novel Scouting for Trolls.This short piece (Terry calls it a "squib") appears to be a smaller part of a larger whole, perhaps a preface to it. Alas, Scouting For Trolls is now fated never to leave the amorphous pool of Invisible Writings to which only very specialised Libraries have access, and we can only speculate on how things might have been.
She is also seen in the Discworld's Assassins' Guild Yearbook and Diary 2000 modelling a detachable exploding bustle: the idea is that the wearer is the delivery system who detaches it in the location where it would most benefit the client, primes it, and discreetly withdraws, albeit in a less full dress.
Interestingly, her likeness, as sketched by Paul Kidby in The Art of Discworld and for the relevant diary/yearbook as cited above, has odd echoes of Roundworld computer game icon Lara Croft. Just as Ponder Stibbon's pencil portrait has a strange distorted echo of a wizard called H***y P****r, we are certain that such likenesses are mere co-incidence existing only in the eye of the beholder. Even after taking into account the bit about her hobby being "stealth archaeologist". Odd similarities to the character of Laredo Cronk in Game:Discworld_Noir have been pointed out, however. A Stealth Archeologist. With the initials "L.C.". Probably coincidence....
An Alice Band is also a hairstyling method involving use of a wide hair-band to push the hair back high off the forehead. It is best seen on depictions of " Alice in Wonderland" (hence the name) and it was very much fashionable in the 1960's.
The Alice Band are a girl-group from Canada who, among other things, did a cover version of that most Discworldian anthem, "Don't Fear The Reaper" . Was this the route that suggested a character name for a lady Assassin?
Here's an interesting piece of ephemera. Alice Band didn't start out as a Discworld character. She originated in a short story he wrote a decade or more before Discworld existed, 'The Great Egg-Dancing Championship'. Alice Band was the sister of Fred Band (Egg-Dancing Champion of Blackbury) and the girlfriend of Jem Stronginthearm (Egg-Dancing Champion of Umbridge), who faced each other in the overall championship for Egg-Dancing (A sport in which you try to dance among eggs while blindfolded. Dancers are scored by the quality of the dance and penalized for how many eggs got cracked). Jem won the match when Fred admitted that his father had swapped out his eggs for fakes that wouldn't break. This story appears as part of the Dragons At Crumbling Castle selection of early Pratchett writings. Evidently the name was recycled later. Thanks to FanFiction writer and reviewer bissek for pointing this out!