READING ACTS: Testament of Levi and the Priesthood (Phil Long). Just to be clear, the Greek Testament of Levi gives every indication of having been written in the second century CE, as a very free translation of the much earlier Aramaic Levi. This is not just a matter of Christian "interpolations," although the new work is certainly Christian. Aramaic Levi has been substantially edited in other ways. Notably, the long section of instructions for sacrificial rites which forms the core of Aramaic Levi has been very much abbreviated in the Testament of Levi. Whoever wrote the Testament of Levi did not find ritual law interesting.
The presentation of the priesthood in Aramaic Levi is problematical. It presents Levi as a priest and a founder of the priesthood in his own time. Yet in the Pentateuch God founds the Levitical priesthood in the time of Moses and the priesthood itself is limited to the family of Aaron (later, of Zadok, Aaron's descendant). More on that here.
The first part of the Testament of Levi basically echoes the view of Aramaic Levi. I am not sure whether Testament of Levi 14-18 is compatible with this view. It seems mostly interested in the Aaronid (Zadokite) priesthood of the biblical and Second Temple periods. But I would have to look into it more carefully to have a confident opinion.
Earlier posts in Phil's blog series on the Old Testament Pseudepigrapha are noted here and links. The last two posts in the series have also been on the Greek Testament of Levi.