Clarke, who put his efforts into the sevens following Super Rugby Aotearoa this year, has been named as a travelling reserve.
The Chiefs player Etene Nanai-Seturo, who was in the same situation, has made the 12.
The men's and women's teams are both full of experience with the women's side including seven players who claimed silver in Rio five years ago.
Co-captain Tim Mikkelson, the most capped sevens player in the game's history, is joined by Scott Curry and Sam Dickson who have more than 50 World Series tournament appearances each.
Their experience is complimented by young talent, including Chiefs' outside back Nanai-Seturo and travelling reserve Will Warbrick, who was discovered at the Ignite7 talent identification tournament in 2018.
Coach Clark Laidlaw highlighted the need for a versatile squad.
"When you've only got 12 players for one tournament, and it could be 40 degrees with high humidity, having players who can rotate and share the load throughout a weekend and still nail their core role is important. We've selected backs who can change positions and that is genuinely important."
More than half the women's team has Olympic experience, while Shiray Kaka and Michaela Blyde were travelling reserves in 2016. Risaleaana Pouri-Lane has a different Olympic experience, captaining New Zealand to a gold medal at the Buenos Aires Youth Olympic Games in 2018.
Since the 2016 Games, the women's sevens team has been incredibly dominant, winning 16 out of 22 World Series tournaments, the Sevens World Cup and Commonwealth Games gold.
"The internal competition we have has really driven this group. We've got a spine that operates really well who we have massive faith in, but then we've got these great young players and players, I describe as hidden warriors, who have been doing a lot of work that you don't really hear much about. It's the drive from all our players to make this squad that has made some of these decisions really tough," said Co-Coach Allan Bunting.
New Zealand Men's Rugby Sevens team:
Tone Ng Shiu
Travelling reserves: William Warbrick, Caleb Clarke, Amanaki Nicole
Non-travelling reserves: Akuila Rokolisoa, Trael Joass, Kitiona Vai, Vilimoni Koroi, Brady Rush, Oliver Sapsford, Moses Leo and Leroy Carter
New Zealand Women's Rugby Sevens team:
Tyla Nathan Wong
Travelling reserves: Tenika Willison, Jazmin Hotham, Terina Te Tamaki
Non-travelling reserves: Dhys Faleafaga, Shakira Baker, Cheyelle Robins-Reti, Manaia Nuku and Mahina Paul
The women are in Pool A and will come up against Russia OC, Great Britain and Kenya, with competition starting on 29 July.
The men are in Pool A at the Olympics and will play Australia, Argentina and South Korea, kicking off on 26 July.