Does the time difference between Jakarta and New York change during the year?

Yes. Because of daylight saving time the gap moves between +11h and +12h.

When is the best time to call New York from Jakarta?

There is no overlap between standard working days, so one side has to call early or late.

Jakarta is 11h ahead of New York. This gap is not fixed: daylight saving time moves it between +11h and +12h during the year.

Jakarta

Indonesia

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New York

United States

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A 9-to-5 working day in Jakarta does not overlap one in New York at all — somebody has to take the call outside office hours.

City	Time zone	UTC offset
Jakarta · Indonesia	Asia/Jakarta	UTC+7
New York · United States	America/New_York	UTC−4

What is the time difference between Jakarta and New York?: Jakarta is 11h ahead of New York. This gap is not fixed: daylight saving time moves it between +11h and +12h during the year.
Does the time difference between Jakarta and New York change during the year?: Yes. Because of daylight saving time the gap moves between +11h and +12h.
When is the best time to call New York from Jakarta?: There is no overlap between standard working days, so one side has to call early or late.