Use your discussion of the event to refer to the question-and-answer portion:

At the ZEE Jaipur Literature Festival in January 2018, I had the opportunity to ask Tom Stoppard a question about his play The Real Thing during the question-and-answer portion of his panel discussion with Sanjna Kapoor (Kapoor and Stoppard).

To create a works-cited-list entry for the event, give the session participants in the “Author” slot, the title or description of the session in the “Title of source” slot, the conference name as the title of the container, and the date and location of the session:

Kapoor, Sanjna, and Tom Stoppard, panelists. Panel discussion. ZEE Jaipur Literature Festival, 24 Jan. 2018, Diggi Palace, Jaipur, India.

If the participants had specific roles, you could organize the entry differently:

Stoppard, Tom, panelist. Panel discussion. Moderated by Sanjna Kapoor. ZEE Jaipur Literature Festival, 24 Jan. 2018, Diggi Palace, Jaipur, India.

Cite a live event only if you attended it. If you rely on the recording as your source, cite the recording:

At the end of the session Stoppard answered questions from the audience about the play (“The Real Thing”).

For the works-cited-list entry, use the publication details of the recording. The recording published on YouTube has been titled “The Real Thing.” List YouTube in the “Title of container” slot, Stoppard and Kapoor in the “Other contributors” slot, ZEE Jaipur Literature Festival as the publisher of the video (as shown on the YouTube page), the date (the upload date shown on the page), and the location of the container (the URL):

“The Real Thing.” YouTube, panel discussion with Tom Stoppard and Sanjna Kapoor, ZEE Jaipur Literature Festival, 1 Feb. 2018, www.youtube.com/watch?v=a32dDSEFYew.

If you cite a transcript of the recording rather than the recording itself, you can list this information in the optional-element slot at the end of the entry:

“The Real Thing.” YouTube, panel discussion with Tom Stoppard and Sanjna Kapoor, ZEE Jaipur Literature Festival, 1 Feb. 2018, www.youtube.com/watch?v=a32dDSEFYew. Transcript.