Hyderabad is 6.5 hours behind Wellington
Best overlap: 2:30 PM to 6:30 PM in Wellington is 8:00 AM to 12:00 PM in Hyderabad.
For a call that suits both sides, look at 2:30 PM to 6:30 PM in Wellington / 8:00 AM to 12:00 PM in Hyderabad. Around 4 hours of overlap is enough to work comfortably, as long as meetings don't drift to the end of one team's day. Finally, Wellington observes daylight saving and Hyderabad doesn't, so this window shifts by an hour for part of the year — recheck it each spring and autumn.