First of all, you should know where you keep your database file. If you're not sure, check out this article: https://www.tntware.com/tntconnect/faqs/en/what-and-where-is-my-database.aspx
Because your TntConnect database is a file on your hard drive, and because you probably have lots of other files that need privacy and protection, we recommend a good disk encryption utility. There are many free solutions, and there might even be an encryption solution built in to your current operating system.
Here's a good resource to let you know what your options are:
TrueCrypt is discontinued, try these free alternatives
If you're concerned about privacy with your files in Dropbox, we'd recommend Boxcryptor to ensure that all your sensitive files are encrypted before they leave your computer and upload to the cloud.