The part of speech that the word, 'will' represents in the sentence is;
A verb is a word that is used to express action. In the sentence above the word, 'will' is an action word that expresses a future action.
'Will' expresses the future action that will be performed by the drama department during fall which has not arrived yet.
The word 'will' can also be used to express a request, facts, or an intention. It can also function as a noun as in this sentence; Diane has a strong will.
Summarily, for the sentence given, 'will' can best be classified as a verb.
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