The phrase "a brief round of" is correct and usable in written English.
It can be used to refer to a short session or occurrence of an activity, often in a casual or informal context.
Example: "After dinner, we enjoyed a brief round of trivia to test our knowledge."
Alternatives: "a quick session of" or "a short bout of".
Everyone broke out into a brief round of enthusiastic applause.
A brief round of applause for minor character Mike Rickk Warden, Catherinee's boss, who isn't as dense and insensitive as she thinks he is.
N.F.L. players and owners ended a brief round of negotiations Tuesday against a landscape dramatically altered by an appeals court decision that allowed the league to continue a shutdown that threatens the start of the regular season.
10.13pm: Dudley brings the press conference to a close, telling his audience both companies are very excited about the alliance, to a brief round of applause before everyone files out to start their weekends.
A month after winning another Wimbledon title, Pete Sampras traded his high-tech racket for some old-fashioned wood today, taking a brief round of batting practice with the Cincinnati Reds.
Before PMQs, which take place at midday on a Wednesday, there is a brief round of departmental questions in which the Scotland, Northern Ireland and Wales offices get their occasional half-hour in the sun.
After a brief round up of the news featuring a photo of Nicky Morgan looking like a dead ringer for a Piero della Francesca Madonna, Stratton started drawing random circles on a screen that Peston insisted on calling Screeny while McVey managed to call Zac Goldsmith's sister Gemma.
Every once in a while, I dive in and do a brief round-up of one of my favorite kind of accessories, USB Flash drives.
There they undergo a first brief round of questioning about their reasons for seeking asylum and have a health check.
At 11 40 p.m. the police returned him to the chief detective's office for a final brief round of recorded interrogation.
WASHINGTON, Oct. 28— The United States looks to the Soviet Union to take the major initiative at what is expected to be a fairly brief round of the talks on limiting strategic arms starting Monday at Hel sinki.
