A player can maybe stop picking improvements for his character…
I'm using a version of Apocalypse World that on page 182 has a section titled The Ungiven Future, which says
You can keep choosing the improvement options in your playbook as long as you like, or until they run out. Starting with your 6th improvement, though, you can choose from these options too:
- get +1 to any stat, to a maximum of +3.
- retire your character (to safety), and create a new character
- create a second character to play, so now you’re playing two.
- change your character to a new type.
- choose 3 basic moves and advance them.
- advance the other 4 basic moves.
(I've included the list in case it's not in whatever playbook you're using and you've already run out of improvements you want.) I don't think it's really in the spirit of Apocalypse World to lawyer the game in the same way someone can lawyer, for example, Dungeons and Dragons 3.5, so putting special emphasis on can keep choosing seems wrong, but that phrase is there, at least implying you can but need not.
Alternatively, you can avoid marking XP a lot of the time just by having your character make different moves. When stats are highlighted at a session's start, during that session have your character make moves associated with different stats. Then, when it's time for you to check your character's Hx with the other characters, rationalize alternately decreasing and increasing your character's Hxs so your character's Hxs remain static. If your character has a move that grants XP, don't have him make it, and if another PC has a move that grants your character XP, tell the player not to have her character make it on your character. Your character's story will probably be very strange, but with careful management (and maybe threats but better to use bribes) your character need never gain XP again and, therefore, never gain another improvement.
…But I suggest arranging things so that's not an issue
There should come a point when you want to retire your character, when he's been through enough, found peace, redeemed himself utterly, succumbed to the depths of despair, or whatever. It's cool if the reason you're jumping through mechanical hoops is because you want to keep playing your character until he reaches that ending naturally rather than him reaching that ending because the game's forcing that ending upon him, but you should also give the MC a heads up to the fact that your character's running out of improvements. That means your character's story's approaching its end, and the MC should include situations that will lead to your character's story's appropriate ending, and you should make bold moves that'll have your character's story conclude in a way that you find satisfying.