Interviewing with a bank after accepting an internship from another division

Hi everyone. I have recently received an offer to join a Supranational bank in their strategy & analytics division. I was happy to get the offer as they have decent internal mobility and their work is worth it overall. Now though, I am interviewing with their banking division for a full-time post. While the internship starts in July and lasts for 3 months, the full-time position starts in October. There is no disclosure requirement on the contract but I still have no idea if it's appropriate to get both. As in, get the internship July-Oct, then take the full-time role afterwards. Anyone has an idea what's the best action here?