First off, I would not explicitly ask for a referral: the partner obviously knows what you want, and will definitely refer you if interested - but making a direct ask could come over as desperate and ignorant of the process.
Instead, focus on what you have to offer, fit with the company and interest in joining. The partner will try to assess the following, in no particular order:
- How well you think: can you help a PL/Principal answer the customer's need and run the required analysis / get to the insight quickly?
- How well you can relate to people: can you listen and build rapport with a customer's analyst to get the data needed to build your next model?
- How much of a team player you can be: Will your colleagues want to strangle you after a couple of late nights in the office? Cf. 'no a-hole' rule
Listen carefully to the partner, ask smart questions (nothing you could find an answer to online; better to ask for an opinion or 'advice to a younger self' for example). Good luck