Asset contribution permissions can be set at a parent folder level and typically inherit down to its child folders unless specifically overridden. So, if you grant contribution rights on the parent "New" folder, those permissions usually apply to all its subfolders as well.
However, please cross check your specific DAM configuration because some setups allow for unique permissions on child folders that can block or modify inherited rights.
In short: Contribution access granted to a parent folder generally extends to its children, but check your system’s permission inheritance settings to be sure.