Using Highcharts with Power BI is typically done using custom events or embedding Highcharts using a generic web environment being referenced by Power BI. There is not a direct connector for specifically Highcharts in Power BI, but this is as follows:
The Highchart Library: You need to have access to the Highcharts JavaScript library. This is the core library that you would typically use to create charts, as it incorporates the whole Highchart framework, modules, and themes that are generally used for customizations. A valid license may be required depending on your case.
Custom Visual Development: Creating a custom visual with the Power BI Developer Tools would bring Highcharts to Power BI. Writing either TypeScript or JavaScript code would allow embedding the Highcharts library into a custom visual framework for Power BI. Power BI has an SDK and tools to cater to that, and you would package and deploy the custom visual so that it's usable within reports.
REST API or Embedded Code: The other way is to set up a web application in which you've done the Highcharts visualizations, then embed that in Power BI either using an iframe or having it as a web content tile. This may also require secure communications through an API or configuring cross-origin resource sharing (CORS).
Data Integration: Ensure that the data in the Highcharts visual receives the same data from Power BI. This can mean exporting the data from Power BI into any standard required by Highcharts or using APIs to fetch live data.