Neesham was due to head to home after the series but a decision has been made for him to return early.
Canterbury’s Cole McConchie was due to travel home following the warm-up matches in England but will now stay on with the squad in England for the duration of the T20 Series.
Black Caps coach Gary Stead said it was important to be flexible at these times.
“We fully support Jimmy’s decision to return home early to be with Alex.”
“The birth of a child is a special time and we are a family environment. We are glad to be able to support Jimmy in heading home.”
Stead said McConchie would bring his strong all-round skills to the squad.
“Cole has impressed us this year when he’s been given opportunities in international cricket and offers any squad options with bat and bowl while also being a strong fielder.”
The first T20I against England is on Wednesday at Riverside, Chester-le-Street.
Revised squad:Tim Southee (c), Finn Allen, Mark Chapman, Devon Conway, Lockie Ferguson, Matt Henry, Kyle Jamieson, Cole McConchie, Adam Milne, Daryl Mitchell, Glenn Phillips, Rachin Ravindra, Mitchell Santner, Tim Seifert, Ish Sodhi.
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