Your example as presented is certainly grammatical and there is no need on grounds of grammar alone to remove been. It is a present perfect passive construction formed by the present tense of have + the past participle of be (been) + the past participle of the main verb (concluded). Conclude is used here with the general sense of bringing a transaction to an end.
Whether you omit been depends on the context and the meaning you’re trying to convey. The passive construction in this case doesn’t tell us explicitly who was responsible for the conclusion of the arbitration. It doesn’t say, for example ‘The arbitration between the claimant and the respondent has already been concluded by those concerned.’ However, it does perhaps leave us with the impression that the claimant and the respondent were involved in some way, even though an arbitration, by its nature, is normally conducted principally by a third party. If, on the other hand, you say ‘The arbitration between the claimant and the respondent has already concluded’ you are using conclude intransitively to mean ‘To come to a close or end; to close, end, finish, terminate’. In doing so, you are putting yourself at some distance from the action, and being even less committed to saying who was involved in the process.
Both are grammatical, so you really need to discuss with the other person what meaning and emphasis the sentence is intended to convey. Much will depend on the nature of the arbitration, who was involved in it, and how much you want to say about their involvement.