The Somerset batsman made his Test debut in the historic win over India this winter and will continue his top-order partnership with Alastair Cook in the March fixtures against the Kiwis.
With just six Test matches scheduled between now and the home series with Australia, which starts in July, Compton is hoping to improve on his unremarkable international career to date.
The ECB have signalled their faith in the South African-born opener by awarding him an incremental contract, but Compton has admitted that he needs to make several big scores against New Zealand to make sure of his Ashes berth.
"Just talking about the Ashes gives me the tingles," he told BBC Somerset. "I need to concentrate on the here and now which is New Zealand. If I do my job then hopefully the rewards will come further down the line.
"Playing against India and walking out with the Barmy Army singing your name was amazing, some of the best moments of my career. It's just given me a taste and I can't wait for New Zealand now.
"I know I need to score runs to keep my place. I expected myself to get a big score, so to make 30 a few times and not push on was disappointing."
Compton scored one half-century and averaged 34.66 in the four Tests against India.