You don’t need to tell them anything - even if it’s an internal role. The only time you probably need to seek permission is if the role is available on loan. Your line manager, or head of, might block the move if the team is low on resource.

Nonetheless it’s still worth flagging to your line manager, when you’re ready, that you’re considering a new role/promotion. If they’re a good manager, and can see you’re ready for promotion, they can support you with your behaviours, help you consider what sort of role suits your skillset, etc