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Just be mindful of this when their turn comes up:
You need at least two hands to climb, but you can cling to a wall with one hand while you cast a spell, shoot a small arm, or take some other action that takes only one hand.
Other than that, I am not aware of some reactionary check to cling to their rope. But if the climber had been Taking 10 to climb because their modifier is low, they might be in trouble now since they'll have to roll.