Yes, some cruise lines will let you leave your kids in the kids club while you are on an excursion booked through the cruise line. Do be aware that the hours of operation may be different on port days than on non-port days.
The cruise lines that will allow this for free are Carnival, Costa (space is limited), Disney , Holland, MSC, Princess and Royal Caribbean.
Norwegian and Celebrity charge a small fee for kids to stay behind port days, and space is limited. Cunard does not allow kids to stay in the kids club while parents are on excursions.