HR administration is basically a clerical job. This makes it difficult to formulate a KPI for this function because most of the employees do not want to take up this profile even though it is one of the most important functions HR. By arriving at a meaningful KPI’s for this profile, the employees in this profile can be evaluated along with others at equal importance there by creating a better lookout toward this profile. Posted by Anil Chilukuri.
What you have described might happen when there is no specifically determined business objectives. Single KPIs without a business context don’t make sense. I was discussing this in the article: https://bscdesigner.com/sound-approach-for-kpis.htm
My first recommendation is to start with building a strategic map where you will map major business objectives (in your case it might be objectives of HR department) and link them with each other showing cause-and-effect relationships between them.
You mention that HR administration is a clerical job. Why it is important? What will happen if HR will stop doing his job? In this article https://bscdesigner.com/the-best-hr-kpis-aligned-with-company-strategy.htm you will find many links to relevant articles about HR KPIs. I think this is a good starting point for your project.