Final answer:
The adverb clause in the sentence is 'after I study,' which modifies the verb 'play' by indicating when the action will take place.
Step-by-step explanation:
Identifying the Adverb Clause
The adverb clause in the sentence 'After I study, I'll play with you' is 'after I study'. An adverb clause is a group of words that functions as an adverb and, consequently, modifies a verb, an adjective, or another adverb. This adverb clause answers the question of 'when' the playing will occur, which relates to the main clause 'I’ll play with you' by specifying the timing of the action.
Adverb clauses typically begin with subordinating conjunctions such as 'after,' 'before,' 'because,' 'when,' 'since,' 'unless,' etc. In the example provided, 'after' is the subordinating conjunction that introduces the adverb clause.