Goalkeeper Nik Tzanev, Nikko Boxall and Dalton Wilkins are the ones to make way, from the squad selected for the games against Curacao and Bahrain last month
Once again, no New Zealand or Australia-based players are eligible for selection due to travel restrictions.
Hay hopes to build on the recent momentum, after the All Whites recorded wins over Curacao and Bahrain.
"It's great we are able to get together again after two good performances last month," said Hay.
"We need to be playing games to develop as a team, especially after such a long break prior to October, so we want to take every opportunity we can.
"These games will allow us to look at a few new players who weren't part of the last window as we continue to build towards Fifa World Cup qualifiers next year."
Hay confirmed Reid will train with the squad and continue in his role mentoring the younger members of the team.
The entire squad are vaccinated against Covid-19, a requirement for playing and training in Abu Dhabi.
In a statement, New Zealand Football said they have stressed the importance of vaccination to all players in contention for the team, as well as informing them that they risk missing out on future selection if they are unvaccinated.
NZF added they will not be releasing the vaccination status of individuals not selected for the team, after Hay confirmed on Saturday that one potential player had yet to be vaccinated.
"At this stage there is a player that hasn't had that, and so we won't be able to select them at this point in time," said Hay. "Everybody's got to make their own choice around that.
But with any choice comes consequences - sometimes the consequences are positive, sometimes they are not so good."
The All Whites face Gambia on Wednesday November 17, along with a warmup fixture on Saturday November 13, with both games to be played at the Zayed Sport City Stadium in Abu Dhabi at 5am.
The All Whites' full 21-man squad:
Stefan Marinovic (26 Caps) Hapoel Nof HaGalil, Israel
Jamie Searle* (0 Caps) Swansea City, Wales
Michael Woud (3 Caps) Almere City FC, Netherlands
Michael Boxall (35 Caps) Minnesota United, USA
Liberato Cacace (5 Caps) Sint-Truidense VV, Belgium
Francis De Vries* (0 Caps) IFK Värnamo, Sweden
Kelvin Kalua (2 Caps) Eastern Suburbs, New Zealand (currently on trial in Europe)
Niko Kirwan (2 Caps) Padova, Italy
Nando Pijnaker (3 Caps) FC Helsingør (loan from Rio Ave FC), Denmark
Tommy Smith (40 Caps) Colchester United, England
Bill Tuiloma (27 Caps) Portland Timbers, USA
Joe Bell (4 Caps) Viking FK, Norway
Matthew Garbett (2 Caps) Torino, Italy
Sarpreet Singh (7 Caps) SSV Jahn Regensburg (loan from FC Bayern Münich), Germany
Marko Stamenic (2 Caps) HB Køge (on loan from FC Copenhagen), Denmark
Joseph Champness (1 Cap) Giresunspor, Turkey
Elliot Collier (2 Caps) Chicago Fire, USA
Andre de Jong (6 Caps) AmaZulu FC, South Africa
Elijah Just (4 Caps) FC Helsingør, Denmark
Callum McCowatt (3 Caps) FC Helsingør, Denmark
Chris Wood (59 Caps) Burnley FC, England
*debut senior national team call-up.
