Question

Shakespeare drew...... folklore for the themes of his plays.

Answer 1

Up -might be the answer

Answer 2

'on' is the most appropriate answer to the question.

"Draw on" is a phrasal verb. The Cambridge Dictionary elaborates it as, "to use information or your knowledge of something to help you do something."

Since Shakespeare used the information derived from folklore for highlighting the major themes of his plays; therefore the most appropriate preposition after drew is 'on' and the complete sentence may be written in the following way.

Shakespeare drew on folklore for the themes of his plays.