Misslaurieloo

Hello! The monkey puzzle tree in my garden had been cut at the top and on the ends of the branches before I moved into my house approximately 3 and a half years ago. The tree has grown significantly in the time I have been here but have noticed a large amount of browning over the last few months, although there is a lot of new growth coming through on most of the branches still. The brown branches seem completely dead while the new growth is very green and healthy looking. The browning is mostly on one side of the tree while there are a couple of odd small branches coming off larger branches which appear dead around the tree too. Is there anything I can do to help the tree? Would it be beneficial to remove the dead branches or would that make the problem worse? Thanks in advance for any help!