Hypersonic weapons have a lot of FUD around them. First off, they aren't some new technology. Most ballistic missiles achieve hypersonic speeds, including the V2 rocket from WW2. What's new are hypersonic glide vehicles that follow a ballistic trajectory up and then are capable of moving and maneuvering down to a target. Notably, this method means that the hypersonic glide vehicle is traveling SLOWER than a ballistic missile traveling to the same target, but the trajectory is depressed and the ability to make some maneuvers complicates targeting and tracking. And that isn't even overly new technology, there have been tests of the hypersonic glide vehicle concept dating back to the 1950s and 1960s. An example of a hypersonic glide vehicle that was actually used was the space shuttle. There's also hypersonic cruise missiles, which are able to achieve hypersonic speeds in level flight.
So what does Russia have? Currently, all they have fielded is the Kinzhal missile. But is it neither a hypersonic glide body nor a hypersonic cruise missile. It is simply an air-launched ballistic missile. It would not be suitable for an anti-ship mission, unless striking a ship docked in port. The impressive and novel thing about it is that they managed to get a ballistic missile to be launched from an aircraft, which is rather tricky to do from an engineering standpoint, and IIRC is the first ALBM to actually be deployed. They also have Avangard in development, which is a hypersonic glide body deployed from ICBMs for the nuclear strike mission. Finally, they have the Zircon missile in development, which is a hypersonic cruise missile meant for the anti-ship mission. Russia claims to have completed testing of the missile, but it doesn't appear to have been deployed yet. It's unclear how effective it would be against a carrier strike group, with air defenses, electronic countermeasures and decoys. Notably, it cruises at a high altitude, unlike most anti-ship missiles which try to skim the surface to make it harder to detect and track on radar.
Ultimately, I don't think that hypersonic weapons fundamentally change the security of the carrier. It may necessitate the development of some anti-missile missiles better tuned for the counter-hypersonic mission. It may necessitate altering doctrine towards the anti-ISR (intelligence, surveillance, and reconnaissance) mission to complicate targeting such missiles. I could be wrong of course!