There are a lot of patron-run book clubs out there. Some are part of senior living centers, homeowners associations, or clubs. It's also true that book clubs take a huge investment of staff time that not every library can afford, especially when attendance can be low. It's possible for library workers to assist local, patron-run book clubs out and to create a hub for book clubs.
The easiest way to do this is online although it can be done with a physical book display and printouts. A book club hub page on your website can be a place to collect information useful to those who run them, curated by your librarians. This will increase the value of your library to the local community, even for those who rarely, if ever, come into your building.
Among the services you can provide is to link to collections of discussion questions found online. Many publishers have resources on their websites as does Book Riot, Oprah Daily, and the website Reading Group Guides. When a particular title becomes popular, you can find a link to specific questions for that title.
Link to videos that show interviews with popular authors. Clubs can view them together which could spur discussion. An example is this Barnes and Noble podcast interview with Stephen Graham Jones discussing Don't Fear the Reaper. Collect a sample of a wide variety of authors, link to the interviews, switching them out on a regular basis. It would be wise to keep a running list of the interviews you have featured in case a patron asks.
Suggestion of titles can be gathered and subdivided by subject, genre, and other factors. Some book clubs look for books of a certain length so consider including the page count. Think about listing suggestions by tone, characters, and setting. As always, there is little excuse for not including a diverse set of authors in lists crafted in advance. Include new titles that would work well for book clubs in a list as well. Listing options in your eBook collection is also a great idea.
Don't neglect younger patrons. Your young adult and children's librarians can assist with information appropriate for a variety of age groups. Encouraging leisure reading during the summer by participation in a book club can help keep reading skills sharp.
Finally, the library can facilitate virtual visits by authors. Organizations like Horror Writers of America have librarian-specific groups which could help arrange a visit. Publishers often have contact information on their website as well. Many authors, with enough notice, are willing to virtually visit with a book club to answer questions and interact with the members. Consider having a librarian be a contact person for book clubs who need more information or assistance with trying to get in contact with an author's representatives.
Consider creating a book club hub either as a supplement to or in place of library-run book clubs. By creating a useful archive of information, you can introduce more people to the variety of services a library can offer.