Taylor's chance comes with Carl Hopkinson, who returned to the England set-up in white-ball cricket earlier this year, currently at the Indian Premier League with Mumbai Indians.
Key suggested both he and Taylor will continue to work with the team in the future.
Speaking to BBC Sport last winter, Taylor said: "I still am not someone who wants the limelight, I just want to be good at my job. That's how I want to go about my coaching really.
"I love being a trailblazer but without the attention. I want to see how far I can go, and work with some of the best players that I can."
The first Test against New Zealand begins at Lord's on 4 June and is England's first in the format since their dismal Ashes defeat.
Amid accusations of the set-up being too slack, England did not have a fielding coach on their staff in Australia, something that came under intense scrutiny when they dropped catches at crucial times.
That campaign, which also included discussion around allegations of excessive drinking of alcohol, brought into question the professionalism of the team set-up, their tactical approach and the futures of Key and coach Brendon McCullum.
A curfew that was introduced for the white-ball tour of Sri Lanka in January will remain in place for the New Zealand series.
McCullum, who has taken time off since the end of the T20 World Cup in March, will be present when the first-Test squad meets for a three-day training camp in Loughborough from 25 May.
It includes bowler Ollie Robinson and uncapped trio James Rew, Emilio Gay and Sonny Baker.
Former New Zealand bowler Tim Southee will not be at the camp but will return as bowling coach for the series against his former side.
Asked what will change in the set-up, given both he and McCullum remain in their posts, Key said: "What we want is to have players to go out and play their best game.
"It doesn't mean there's one way of playing, where you go out and play shots.
"I spoke to Emilio Gay this morning and said 'go and play your best game don't worry about anything else'.
"Work out how you are going to take on that bowling attack at Lord's, work out conditions and your best way to score. The same for everyone else.
"You do not want to see what has made Harry Brook go to number one in the world change. You just want him to refine."

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