The 'Arbiter General was a senior official of the Federation's Justice Department. It is possible that he was the chief law officer of the Federation and legal advisor to the Administration, with perhaps some powers relating to the judiciary. While there is no direct evidence for such powers, they may be implicit in the very title 'Arbiter General' and in the activities of Ven Glynd.
The title 'Arbiter General' is suggestive of the office of 'Attorney General', which exists in many states on Earth. While the powers of the various Attorneys General vary, all of them are at least the chief law officer of that state, as well as the legal advisor of that state's government. The use of 'Arbiter' as part of the title suggests some judicial role.
Ven Glynd's activities indicate that he wielded considerable power. He organised the manipulation of the evidence in Blake's trial, as well as appointing Tel Varon as the latter's defence counsel. He also had the power to order an inquiry into Blake's case, and perhaps to consent to the issuing of a holding order. Once Varon was aware of Ven Glynd's true role regarding Blake, he told Maja that they would have to go 'Higher up. Even to the President if we have to', suggesting the possible existence of a superior between the Arbiter General and the President, perhaps a Minister for Justice or an equivalent; and his next remark, about needing 'the strongest possible evidence' is again suggestive of Ven Glynd's high office.
After Ven Glynd defected from the Federation, it is clear that he was a key mover with Le Grand] in the conspiracy, having spent an unspecified period of time using his position to gather evidence of the Federation's injustices. His presence in the conspiracy convinced Blake that it was a serious proposition. Of interest is the fact that he was still referred to as Arbiter General, which presumes that the Federation did not want to advertise the fact that it knew of his defection to the rebels.
To the above evidence must be added a possible disclaimer. Ven Glynd was never referred to as Arbiter General at the time of Blake's trial, perhaps suggesting that he might not have held that office at that time.