As far as I know the MHA Tribunal is a small court with a Judge, a doctor and a lay person. They listen to a case where two parties clashes, where one is imposing a MHA Section of compulsory detention and the other disagree. The outcome of this tribunal, usually, is either upheld or discharge the MHA Section.
If the compulsory detention is upheld then the patient has the right to appeal the decision. And this scenario has happen before.
But, if the decision is to discharge from section, then can the doctor has the right to appeal the decision from the tribunal?
Taking into account that the right to appeal is the right to ask a court or other official body to consider changing a decision that you disagree with.
You cannot appeal against the Tribunal’s decision merely because you disagree with it, but you can ask for permission to appeal if you think there was a legal mistake, such as if the Tribunal did not apply the correct law or wrongly interpreted the law, did not follow the correct procedures, or had no evidence or not enough evidence to support the decision that it came to.
I agree with Guy’s answer, though strictly it would be the responsible authority rather than the RC/doctor who would challenge the decision. There is some more information on MHLO here: Appealing against a tribunal decision (MHT).