There are some other liquid deterrents other than Bitter Apple and sometimes a different one will work. You can also try a little hot sauce or even spray starch will work for some puppies. I am not clear on what the gate is for, if it is part of confining him and the other solutions don't work then you may want to switch to a metal gate as wood splinters don't often pose a threat but occasionally we do see pets with perforated intestines which is a major problem. Also, chewing the gate could be an attempt to get out or it may just be boredom which can sometimes be avoided by adding interactive chew toys such as Kong Quest or Traxx, Nylabone Romp n Chomp or Starmark Everlasting. The best solution may be a metal gate if you need it long term.