According to the insider, the project transpired swiftly, with the video’s tone appealing to Paltrow among other elements.

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...