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I'm pretty sure that if you asked your compliance officer, they would tell you that there is no requirement to declare / disclose / attest to any gambling, either to them or the regulator, even as an approved person.
Political donations are, as I understand it (having clicked through interminable training slides) acceptable, provided there is proper due diligence vis. bribery and / or corruption.
I'm going to have a look to see if they are counted as COIs at my current shop.
Well, I'm no expert, and it's entirely possible I'm confusing 'potential COI' or maybe 'situation which may risk a COI' with 'COI', but I believe the FCA says that being an employee (of any kind) of a UK financial institution and making any personal donation to a US political organisation is a Personal Conflict of Interest which must be declared. But again, that's a specific legal or regulatory definition.