The clip, which showed Byron and Astronomer’s HR head Kristin Cabot in what appeared to be an intimate exchange, sparked a massive controversy online and led to significant personal and professional fallout.

Tech company Astronomer is trying to move on from its Coldplay concert kiss-cam scandal with the help of a Madison Avenue powerhouse known for his sense of humor.

“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...