No. You can’t share a folder that’s inside of a shared folder unless you’re using a Dropbox Business account.
Dropbox Business team members can share folders that are inside of team folders, which is a type of shared folder that’s only available to Dropbox Business users. Team folders can only be created by an admin. Learn how to find and contact your team's admin.
Dropbox Basic, Plus, Family, and Professional: Other options for sharing subfolders of shared folders
You can’t share a folder inside of a shared folder, unless you’re a Dropbox Business user. However, you do have some other options: