You can only see people on the Directory who are in your own stake -- there is no way to see anyone in another stake (unless you have a calling in another stake, such as a YSA bishopric).
Why not? The privacy policies of the Church, which are affected by privacy laws in many countries.
Certain clerks and leaders can use CDOL to look up contact information for a limited set of leaders and others in other stakes.
If you could give us a better idea as to why you want to look up people in other stakes, perhaps we could give you more specific suggestions.
Questions that can benefit the larger community should be asked in a public forum, not a private message.