That’s tighter still, but I think the ‘former students’ line might imply that they’re going to be a feature of the trilogy, which they aren’t. Maybe a better angle would be to focus on the First Order somehow being more cohesive, extremist, and more of a threat than the other Imperial remnants? And/or something about the Republic not wanting to break the peace, hence the secrecy?

Something like-

“Not wanting to break the tenuous peace with the remnants of the former Empire, but fearing the rumoured rise of an extremist faction, several in the New Republic Senate have secretly authorized a daring task force to resist the rising threat.” -??

“Not wanting to break the tenuous peace with the remnants of the former Empire, several in the New Republic Senate have secretly authorized a daring task force to resist the rising threat of a rumoured extremist faction called the FIRST ORDER” -??

“Not wanting to break the tenuous peace, several in the New Republic Senate have secretly authorized a daring task force to resist the rising threat of the FIRST ORDER, a rumoured extremist remnant of the fallen Empire.” -??

You could maybe even bring something in to show that the Republic is largely demilitarised?