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

Yes. Because of daylight saving time the gap moves between +8h and +9h.

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

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

Dubai is 8h ahead of New York. This gap is not fixed: daylight saving time moves it between +8h and +9h during the year.

Dubai

United Arab Emirates

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New York

United States

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

City	Time zone	UTC offset
Dubai · United Arab Emirates	Asia/Dubai	UTC+4
New York · United States	America/New_York	UTC−4

What is the time difference between Dubai and New York?: Dubai is 8h ahead of New York. This gap is not fixed: daylight saving time moves it between +8h and +9h during the year.
Does the time difference between Dubai and New York change during the year?: Yes. Because of daylight saving time the gap moves between +8h and +9h.
When is the best time to call New York from Dubai?: There is no overlap between standard working days, so one side has to call early or late.