A notion of an instant in time that advances linearly without any ambiguities, which would be TAI, and a notion of the precise orientation of Earth, which would be UTC.
To record events, you will use TAI, to point your telescope to a celestial object, you will use UTC.
Astronomers don't really use UTC for pointing telescopes though, they use sidereal time. A sidereal day is 4 minutes different from a mean solar (UTC) day, so you still have to do a conversion.
You still need something that keeps track of the Earth's rotation, but presumably the ITU will still keep track of the difference between UT1 and UTC. I'm an (ex-) astrophysicist, but I'm not convinced that astronomy would actually be particularly impacted if leap seconds would stop being applied to UTC. You already need to keep a leap second table, it would just shift where you apply it.
A notion of an instant in time that advances linearly without any ambiguities, which would be TAI, and a notion of the precise orientation of Earth, which would be UTC.
To record events, you will use TAI, to point your telescope to a celestial object, you will use UTC.