If you go to Setup > Processes > Action Rules, you should be able to create one.
I don't know if this would actually work or not, but you could try doing an action rule that is triggered only when client updates a ticket, and the criteria is something like Updated by client "blank" within the last "blank" business days. This should catch all the updates.
Then have the action modify the ticket, and set the due date to 'Default for ticket priority' which I assume would be one day.
Again, I am not sure if this would actually work like I think it would, let me know if you need screenshots, I might not have done the best job explaining myself.