If there isn't one why not? It seems like a reasonable thing to have. I am doing a lot of experimenting, being new to Hubitat, and the logs are becoming a mess.
There isn't a "clear logs" option that'll delete existing logs, if that's what you're looking for. You can filter the logs by selecting the app or device that you want to see. You can also click on the app number (app:xxxx) or device number (dev:xxxx) at the very left of the log file to filter on that specific item. Probably not the answer you wanted but I hope the filter option will help.
If you really do want to clear the logs, you can make a backup, do a soft reset and select the "clear past logs" option while you're doing so, and then restore that backup when you're done. That's probably a bit time-consuming for something that normally doesn't matter that much; keep in mind that search/filter capabilities are available (by device/app, log level, etc.) and that past logs will eventually clear themselves out on a size-based limit.
But a soft reset is a safe action to perform as long as you restore a backup (and don't reset anything else, notably, the radios) -- and it can do what you're asking if you really want to.
That only removes what is currently displayed on the Live logs page. It doesn't actually delete anything from the logs. The Past logs page will show the data still resides in the logs.