I want to install Drupal 7 in a new directory of my site, using the same database account used in my previous Drupal site. Will this cause any data loss?
If you are going to move the Drupal files from a directory to a sub-directory, you should not have problems of lost data, which means the database still contains the data for user accounts, and for the created nodes.
Keep in mind, though, that some database tables contain absolute paths/URLs. Moving Drupal files to a sub-directory means that some URLs change, such as the ones to access uploaded files. The cache for the visited pages contain the absolute URL of the page; changing the directory where Drupal is installed means changing the absolute URL of pages, and not allowing Drupal to get the page content from its cache.
I would not talk of lost data, but rather of database references that need to be updated.