You have several options. None of them are exclusive to Kanban though. They all work perfectly fine with Scrum too.
- Story Points (start where you are!)
- Avg. Number of Cards Done / time unit (avg throughput)
- Cycle Time & Lead Time
Remember, Kanban isn’t a project management methodology. It’s a continuous improvement methodology. Change things as needed, but do so empirically. Run small experiments and measure the outcome. I’d start by continuing to use story points while simultaneously collecting the other measurements. This allows you to compare the two and be confident in your new metrics.