Trade Consulates cost $500, but aside from this they are purely beneficial.
The most immediate benefit is the right to set trade policies such as subsidies to encourage trade. Trade policies are set using the tab with the ship icon on the right side of the screen.
Once a new trade consulate is established in a nation, each completed trade deal between your Empire and this nation causes an improvement of your diplomatic relationship. If relations improve enough, some of the Council votes of the other nation might go to you. Eventually, their leaders could decide to join your Empire peacefully.
Finally, a trade consulate allows the later construction of an embassy. Embassies, although quite costly, offer even greater control over diplomacy.