Kristin Cabot has resigned from her role as chief people officer at Astronomer, a week after a video of her cuddling up with CEO Andy Byron at a Coldplay concert went viral on social media.

Paltrow always seems be in on the joke.

“Astronomer has gotten a lot of questions over the last few days and they wanted me to answer the most common ones,” Ms. Paltrow says directly to camera in a video posted on Astronomer’s social chann...