Spar urethane is commonly used to finish most chainsaw carvings. Slightly thinning the material with paint thinner allows for better absorption into the wood. This product can be picked up at most hardware stores and larger outdoor/home repair stores. I commonly tell customers to clear coat their carvings at least once a year. Timber oil is another natural preservative commonly used to keep your carving looking brand new.
Preventative maintenance such as clear coating is just like treating wood on your house. When splits or checking occurs, the newly exposed wood needs to be treated. Sealing the carving allows the water inside the wood to evaporate slowly, reducing the size of cracks or checks as the wood dries out. If the carving is going to be outside, it should NOT be placed directly onto the ground. This allows moisture into the log and will eventually cause rot. Keeping the piece on a garden paver stone or in an area that can drain pea stone; is a good way to reduce this from happening.