Insights is a way to store and retrieve data, as well as crafting meaningful dashboards for your use cases. Insights itself does not collect data, outside of the Insights Event API, which allows you to insert custom events. It’s possible you could create a script that captures this data and use the aforementioned Event API to send it as custom events to Insights.
What sort of applications are your clients connecting to? If it’s already being monitored by a New Relic product, let us know what product that is. It’s likely that, if you want to collect TLS data about your clients, using that data-gathering tool would be your best bet.
Once we know how your clients are connecting and what product/products are being used currently, we can loop in the appropriate experts to help answer your question.