"remaining vestiges" is correct and usable in written English.
This phrase is typically used to describe remnants or traces of something that used to exist but is now mostly gone or forgotten. Example: The abandoned building was the last remaining vestige of a once-thriving industrial town.
Whom is one of the few remaining vestiges of Old English's rich case system.
In many parts of the world, protected areas contain the remaining vestiges of intact ecosystems.
The Conservatives are offering the gay community no new measures to remedy the remaining vestiges of homophobia and transphobia.
Whatever your stance, the ground stands as one of the last remaining vestiges of 20th century Sydney rugby league.
Likewise, the British realized that they had lost any remaining vestiges of control and began to speed up their exit strategy.
And also, probably, because of all the remaining vestiges of a past as an arts district on par with today's West Chelsea.
But on Sunday, Rodgers slammed the door on any remaining vestige of the Favre era in Green Bay.
One remaining vestige of such fairs is found in the county, agricultural, and livestock fairs that are still popular in the United States and in Europe.
"All of this has been done without even a whimper from the Liberal Democrats, who have lost any remaining vestige of credibility on civil liberties".
Having unambiguously nailed the IOC's colours to the mast of anti-doping, will this remaining vestige of Olympic values be sacrificed, too?
The two-day meeting will start on Wednesday and focus on stalled joint projects, such as a factory on the border that was the last remaining vestige of inter-Korean rapprochement until Pyongyang pulled out its workers in April.
