I'm assuming it's someone within ONI, because they seem to be the ones who hold the most power according to what's going on in the lore right now.
From what I gathered from the scene, this unknown person is trying to "perfect" the Spartan IV's (or maybe a new, special group?) like the Spartan II's arguably were. So that is why Halsey is being interrogated about her work on the Spartan II's and particularly John (who, let's face it, is humanity's greatest hero at this point in time). I'm sure more will be revealed rather within Spartan Ops itself, or maybe it will become a major plot line for Halo 5/6? We'll just have to wait and see.... --- IRON MAIDEN IS MY RELIGION! Gamertag: Demigod Elessar