If you have chopped down all the trees on your Home Island, you should wait until new ones have grown. It may take some time, as it happens in real life. Every day one to three new trees of different types (fir trees, oaks etc.) will appear on your Home Island.
Note: please make sure that you have enough space on your Home Island for the trees to grow! You need to remove the tree stumps that are left once trees have been chopped. Only after that, new trees can grow. Also make sure that you don't have a lot of resources or gift boxes laying on the ground around the island - that also interferes with tree growth.
We recommend striking a good balance, accumulating resources for future use and looking for resources on other islands.