Hope had innings of 16 and 43 in the first Test win over Zimbabwe but managed just one in the laboured second Test draw in Bulawayo.
Ambris, 24, has yet to play Test cricket and has made just one appearance for the ODI side.
"Sunil has replaced Kyle Hope in the squad, and this is on the basis of his consistent performances across formats and his outstanding returns for the Windies ‘A’ Team," said West Indies chief of selectors Courtney Browne.
"Kyle is encouraged to return to the first-class championship and turn in the strong performances his talent suggests he can deliver."
West Indies will face New Zealand in Wellington from December 1-5 and at Hamilton from December 9-13.
Squad: Jason Holder (captain), Kraigg Brathwaite, Sunil Ambris, Devendra Bishoo, Jermaine Blackwood, Roston Chase, Miguel Cummins, Shane Dowrich, Shannon Gabriel, Shimron Hetmyer, Shai Hope, Alzarri Joseph, Kieran Powell, Raymon Reifer, Kemar Roach.
Alzarri JosephDevendra BishooJason Holderjermaine blackwoodkemar roachKieran PowellKraigg Brathwaitemiguel cumminsnew zealandRaymon ReiferRoston Chaseshai hopeShane DowrichShannon GabrielShimron HetmyerSunil AmbrisWest Indies
First Published: November 6, 2017, 9:54 AM IST