Besides Neesham being ruled out, arrival of veteran offspinner Jeetan Patel, who has been called in as a replacement for injured Mark Craig, is also delayed.
Neesham's recovery is being monitored and giving an update on him, New Zealand team media said, "At present he's not fit for the Kolkata Test. But we are monitoring his recovery constantly and at the moment can't say whether he would be out for the entire series. We will take a call on him before the third Test (in Indore)".
"We are not able to get any replacement in time who is a batting allrounder. Unfortunately, we have got a few other injuries at home as well, which makes that really challenging," he said.
Meanwhile, Patel will arrive not before late tonight as his flight earlier got cancelled.
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"Unfortunately his flight from England got cancelled as he has boarded another flight and will arrive late tonight," NZ media manager told PTI.
This means Patel will have just a little over 24 hours to acclimatise before becoming New Zealand's third spinning option for the crucial second Test, which they must win to save the three-match series having lost the opening game by 197 runs.
Coach Hesson has hinted at a three-spin attack here at the Eden Gardens, where the ball stayed low and slow with a reasonable amount of turn during the T20 World Cup.
"It's going to be hot and humid again and the pitch will deteriorate pretty quickly," Hesson said.
"A lot of (spin bowling) is about the pace you bowl. In New Zealand, because the wickets don't turn, we try to beat batsmen in the air. They don't even contemplate that here -- they try to beat you off the wicket. And if you are unable to score runs, they create more pressure by putting more and more fielders around the bat."
"We are not smacking each other over and talking about all the bad things. We got confidence from large parts of the Test," he said.
The visiting team, who opted to take rest today, will have their first practice tomorrow afternoon.
The Black Caps had the first blow when pacer Tim Southee injured his ankle even before the three-day warm-up game in Delhi. It was followed by Craig suffering a side strain while bowling in the second innings of the Kanpur Test.