The fields in a directory part display based on a handful settings. 
 
The Public by default setting within Administration > Field Options
Set the default behavior for maintaining the privacy of constituent data on your website. These settings determine which directory fields are visible to other members of the community, when no explicit privacy preference is set by the user within their Profile Form. 
See our documentation here to change the Public by Default options. 

If new users are added while the field options are set as public, the fields will be marked as public.  If new users are added while the fields are marked private, their fields will be private. If privacy edit is enabled for Profile Forms, the user has the ability to change the privacy of the fields. 

If a change is made to make the field public or private by default, the following may or may not be affected:
  • Changes will only affect new records or records which do not have a linked NetCommunity username
  • Changes will not retroactively change this for existing records, who have a linked user to NetCommunity, in a directory or profile form
  • Changes will affect Organization constituent records at any time
  • Changes will not retroactively affect records who have a NetCommunity username/password, including users who have a deleted username

The privacy settings the user set on their Profile Form

If the user has a linked account between NetCommunity and The Raiser's Edge, and they choose the privacy of their fields to be public or private, the directory part respects their privacy choice. If a field is blank in the directory, but you want it to be public, the associated linked user will need to log into NetCommunity, access their Profile Form and update the privacy of the field. 
See how to set privacy as an individual for more information.
See the bullet points under The Public by default setting within Administration > Field Options for scenarios where the fields may update for non-linked users.