Not personally, on a standard organised expedition cruise. The operator handles the voyage's advance notifications, environmental approvals and operating authorisations. That doesn't mean Antarctic tourism is unregulated. It runs under the Antarctic Treaty System and the national laws implementing it, and the permissions exist at the level of the expedition rather than the passenger.
Where passenger-level action can be needed is the unusual stuff: private expeditions, yachts, filming projects, scientific work and drone use can all require separate approvals. Your own nationality can also create additional notification obligations, particularly on a private expedition rather than a commercial voyage.
If your trip involves anything beyond being a passenger on a scheduled sailing, ask your operator directly whether anything is required from you.