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I'm DM-ing an adventure, and my players are about to hit level 4, where the first ability score increase happens. If my monk chooses to increase their dexterity or wisdom, will their AC increase as well?

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Yes, their AC is adjusted

Per the rules of Unarmored Defence

Beginning at 1st level, while you are wearing no armor and not wielding a shield, your AC equals 10 + your Dexterity modifier + your Wisdom modifier.

It is based on their current Wisdom and current Dexterity. If they drink a potion that increases their Wisdom, their AC goes up. If they get hit by an undead that drains their Dexterity, their AC goes down.

It is not based on the scores when they are first level. There are many features that scale as the character's abilities improve, such as hit points retroactively increasing when the character's Constitution is increased.

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    \$\begingroup\$ "It is a feature that scales as the character improves." Suggestion: "It is one feature among many that scale as the character's abilities improve, such as..." (The first one that comes to mind is the hp bump applied retroactively for all levels when Con increases) \$\endgroup\$
    – Kirt
    Commented Jul 11, 2023 at 17:20
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    \$\begingroup\$ @KirtnoQA4mewhilemodsstrike, added \$\endgroup\$
    – MivaScott
    Commented Jul 12, 2023 at 6:51

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