Yes, the Barclays Center is still holding private events

The community notice for February 2019 events at the Barclays Center did not include, as has been the practice, any private events. The logic for including them is that some draw large crowds and neighbors should be alerted.

But that doesn't mean there aren't any private events. A 2/7/19 Amsterdam News article, Spreading the gospel of HBCUs, cites an event today/tonight launched by Andres “Dre” Martin, who's now a Brooklyn Nets Account Manager:

HBCU Night, an event touring the nation that celebrates African-American Heritage and the culture of historically Black colleges and universities.
...His latest event is taking place this Friday at the Barclays Center in Brooklyn. It will consist of a panel discussion with HBCU alums at the top of their game, a college fair, networking event and a career fair for HBCU alums in the city. The event is touring to other cities in the coming weeks.

It's not a huge event--such nights have an average attendance of 500--but it involves both attendance at a Brooklyn Nets game as well as earlier-in-the-day events at the arena:

Alumni Mixer 6:30PM-7:30PM // Billboard Lounge: Private cash bar available (All tickets to this event must be purchased through the link or representative. MUST BE 21+ TO ENTER ALUMNI MIXER)
D&I Workshop for selected HBCU students, HBCU Fair (1PM-2:15PM) & Private Panel (2:30PM-4PM) for prospective college students and current HBCU students will run from 1PM-4PM // Large Boardroom and 40/40 Club