The granting of a trade consulate to a minor nation gives you the right to build an embassy there. Although you may not be able to afford it yet, embassies are extremely valuable.
Use the overtures (scroll) tab on the right side to establish an embassy. Click on the embassy scroll and then the nation selected for the embassy. A small diplomat's hat will appear confirming the order.
It costs $5000 to build each embassy. Embassies permit full-fledged diplomatic relations including granting foreign aid, pacts and other treaties, and the possibility of armed intervention if the minor nation is invaded.
Only those minor nations with embassies will ever consider joining your Empire voluntarily.