I think this is one of the most heartbreaking and revealing moments in the premier, but it’s over so quickly that if you blink you might miss it.
Katara was expecting Tenzin to come and stay at the South Pole and teach Korra Airbending. Her son was going to be staying with her and her three grandchildren would be around and playing together. Instead plans suddenly change and all of a sudden Tenzin will leave immediately. Katara obviously doesn’t say anything, she trust her sons judgement and wouldn’t possibly stop him from leaving.
But I think this moment says a lot. Katara is an incredibly strong women. But she has also lost a lot now. Her brother is gone. Her husband who she was together with for over fifty years has passed. And all of her children have left and are leading their own lives now. She had the opportunity to finally be accompanied by her family and they have to leave unexpectedly. In this brief moment we see that it does affect her, that’s she’s sad and that she’s definitely going to miss them.