According to the core Numenera rules, XP can be spent in four different quantities. As far as I can see only the 3XP choice is definitely inappropriate for a short game.
- 1 XP can be spent to re-roll any die roll in the game. Really any roll --
not only a roll made by the player spending the XP. 1 XP can also be spent to resist a GM intervention. Both of these are obviously useful in a game of any length.
- 2 XP can be spent on temporary
benefits of the type "trained in [skill] in [specific location]." I could
imagine this could be really useful in a one shot. At the GM's discretion 2XP can also be spent on a numenera item only useful for one scenario. Both of these are specifically triggered by immediate in-game events/needs, so are very appropriate in your case.
- 3 XP can be spent on a variety of long-term benefits that specifically require considerable time investment first (familiarities, contacts, a home, an artifact), so these are inappropriate for a short game.
4 XP can be spent on a more traditional level up, where there are four options, each of which can only be taken once per tier (so, in the case of a short adventure, only once).:
- Increase effort by 1
- Spend 4 points on increasing pools (divide 4 points as desired)
- Increase one edge by 1
- Become trained in a new skill, or specialised in one you are already trained in
- There is also the option for 4XP to replace one of options 1 to 4 with reducing your armor cost by 1 or increasing your recovery roll by 2.*
The 4XP ones could certainly be useful even in a limited game, though I guess it's up to the GM to call whether such improvements can happen in the middle of an adventure.
* Any of the 4XP level ups can also be replaced by choosing an additional nano/glaive/jack ability, but I'm guessing you can't do this with the starter set as I suppose you're working with pregens.