Does the time difference between Hong Kong and Karachi change during the year?

No. The gap stays at 3h all year.

When is the best time to call Karachi from Hong Kong?

Between 12:00 and 17:00 in Hong Kong, which is 09:00 to 14:00 in Karachi.

Hong Kong is 3h ahead of Karachi. This gap is the same all year — neither city shifts its clocks relative to the other.

Hong Kong

Hong Kong SAR China

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Karachi

Pakistan

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A 9-to-5 day in each city overlaps for 5h. That is 12:00–17:00 in Hong Kong, which is 09:00–14:00 in Karachi.

City	Time zone	UTC offset
Hong Kong · Hong Kong SAR China	Asia/Hong_Kong	UTC+8
Karachi · Pakistan	Asia/Karachi	UTC+5

What is the time difference between Hong Kong and Karachi?: Hong Kong is 3h ahead of Karachi. This gap is the same all year — neither city shifts its clocks relative to the other.
Does the time difference between Hong Kong and Karachi change during the year?: No. The gap stays at 3h all year.
When is the best time to call Karachi from Hong Kong?: Between 12:00 and 17:00 in Hong Kong, which is 09:00 to 14:00 in Karachi.