Nathaniel Taylor had a skull of a giant carnivorous dinosaur under his desk seen first in the episode "Genesis", it did not have the crests of a Carnotaurus and was too big for an Acceraptor, so it may have been a type of large Allosaur, such as one of the types discussed below.
As the genus Allosaurus lived only during the Jurassic Period rather than the Cretaceous Period when Terra Nova is set, and as the characters referred to it as an "Allosaur", this dinosaur is probably some other genus from the superfamily Allosauridae, each of which can be described as a type of Allosaur. For example, it could possibly be an Acrocanthosaurus or Carcharodontosaurus or Giganotosaurus, each of is a genus from the Allosauridae superfamily that lived in the Cretaceous, though Carcharodontosaurus and Giganotosaurus fossils are known from a time slightly closer to that of the show than Acrocanthosaurus (Carcharodontosaurus and Giganotosaurus were also two of the largest predatory dinosaurs, larger than Tyrannosaurus Rex, as mentioned in this wikipedia article, and Acrocanthosaurus is also high on the list). Carcharodontosaurus is known from Africa while Giganotosaurus is known from South America, and since Carnotaurus is only known from South America this might make Giganotosaurus more likely, though as mentioned in this article the two continents were joined until the Middle Cretaceous (Acrocanthosaurus was from North America, which had broken away from South America and Africa during the Jurassic, although see the Science & Speculation section of the Ankylosaurus article for a discussion of the possibility that animals could have migrated across a land bridge between the Americas in the Late Cretaceous). Compare the skull under Taylor's desk with the Carcharodontosaurus skull in this image and the Giganotosaurus skull in this one. The skull of Acrocanthosaurus could also be a possible match, as it shares the distinctive ridge in the antorbital fenestra, the large opening in front of the eye sockets (though a similar ridge seems to be present in the Carcharadontosaurus skull at the bottom of this page). For a size comparison, a photo of a person standing next to a life-sized Acrocanthosaurus skull replica can be found here.
The Allosaur could also be another known genus found in the Allosauroidea superfamily (there is some debate about which types to put in this superfamily, as discussed here), or it could be another genus of Allosaur that was never found in the fossil record.
Alternatively to being a carcharodontosaurid, most of which were extinct by the time of Terra Nova, the Allosaur could instead be some kind of neovenatorid, a group of Allosauroids with some species that were alive up until the very end of the Cretaceous. Some neovenatorids could have reached very large sizes, like Siats and Deltadromaeus, although they lived slightly earlier than when the series is set.
A much more accurate representation would be classifying it as a megaraptoran, a group of theropod dinosaurs, whose classification is still uncertain, as many debate if it should be attached to the coeluosaurs or the carnosaurs. Megaraptorans were very common around that time, like, for example, Tratayenia.
