Where an employer recognises one union can a worker ask to be accompanied by an official of another union at a disciplinary or grievance hearing?

Yes. There is no requirement in s.10 of the Employment Relations Act 1999 that a trade union official who accompanies a worker at a disciplinary or grievance hearing must be from a recognised trade union. The official must simply be either a trade union official employed by the union, or a lay trade union official whom the union has reasonably certified in writing as having the necessary experience or training to act as a companion at disciplinary or grievance hearings. If the worker is a member of a non-recognised trade union, the worker may therefore ask to be accompanied by a trade union official from that trade union. While there is no requirement in the legislation for the worker to be a member of the relevant trade union to be accompanied by one of its officials, in practice trade unions rarely support workers who are not their members.