As Guest55 says, the head of the primary school could attend in support of the parent, but this is actively discouraged in some authorities as a written statement of support can be provided.
Here in Gloucestershire, at the appeals I've heard:
Primary School KS1 admission. The LEA presented the case, but the head came to give evidence regarding the schools capacity and details of problems with the cohort.
Grammar admission. I've never seen the Grammar head teacher at the appeals. He used to come in after we'd made our decisions to say Thank You to us for being on the panel, but now that does not happen.
There was one appeal where the head of a private school came to support the parent. It was a very unusual emotional case, and the evidence the head gave was not in relation to academic ability (that was all written). We often get appeals from that school, in fact even had a couple of other ones in the same round of appeals. The other parents appealing were aware that the head was supporting that one appeal, and knew why, and we've never seen her before or since. We were aware that her attendance did not reflect on her level of support for the other appeals.
To sum up, it's very unusual.