Limited experience on the specific matter, but I'd personally I'd be looking for far broader leadership / interpersonal skills for someone to head up a primary school - not at all necessarily any familiarity with non-routine HR tasks other than knowing where to go for getting and following proper third party guidance

One of the key HR tasks is dealing with teacher performance. I think it’s quite tricky to set a task but certainly the interview questions should be including something around how they have dealt with a teacher who is underperforming. Are you a local authority maintained primary or an academy? If the former, presumably you have support from the authority who could certainly be able to advise on appropriate tasks. Also there is guidance on Headteacher recruitment developed by the DfE in conjunction with the NGA together with a toolkit which might be worth looking at.

In reply to Nicola:

Thank you Nicola. There are a wide variety of tasks and interviews set up. The CEO would like an HR task and a finance one. Just trying to get some thoughts should anyone have had to do one previously.