A large number of draws on her time

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Senior Member
Hi everyone,
here's the sentence that has got me stumped:

«As director of national intelligence, she was the chief intelligence officer of the United States, and with this role quite naturally came a tremendous amount of responsibility and a large number of draws on her time

Is it something like wasting one's time? She's is so busy that she has lots and lots of things to do and places to go to, ecc. But I'm not sure, at all.

Thank you in advance,
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