Note that the presence of a tradepost gives the republic casus belli to try and seize the city in this county, and them owning the city in your county gives them casus belli to seize the county, so it can be a bad idea to allow a non-vassal republic to set up in your realm unless you are stronger than them. Your options are to embargo war them for an instant cash injection on success (the tradepost will be destroyed) or leave the tradepost/s and probably benefit more over time. Assuming you or your vassals control the relevant cities then you benefit from the presence of trade zones.
Trade zones give bonus income to any adjacent tradeposts and coastal cities (not forts or temples). I'm assuming you're tribal or feudal, if you're a repulic then you should ignore the following and take the tradepost for yourself. (Edit: not pasta, typing this took a while :P)
