Somerset batsman Compton struck a second successive century as he and Trott shared a 210-run partnership on the opening day of the second Test against New Zealand in Wellington.
Compton, who had previously only made one fifty in eight Test innings, now seems to have established himself in the England top order.
However, Trott has stressed that the 29-year-old must not "rest on his laurels" if he wants to feature against Australia later this year.
"It's fantastic for him but there's a lot of cricket left this year," Trott, who ended day one unbeaten on 121, told BBC Sport. "You have to wake up tomorrow ready for another challenge.
"He's worked extremely hard in county cricket, and now on the international scene he's been given a chance to open the batting - and scored two big hundreds that have meant a lot in the context of the series.
"You never know about [his place in the Ashes team]. There are so many things that go on in cricket; you can break a finger or something like that. No-one's got a divine runs to score runs or have good form. It's all about taking your chance and being positive when you get it."
You can follow Sports Mole's live commentary of the second day in Wellington by clicking here.