If I understand correctly, you researched and activated a technology for a city expansion in your research tree.
If you click on the build menu icon, towards bottom center on your screen (short cut, press B), then click on expansions tab, is the middle expansion option greyed out?
If it is, this means you do not have enough coins to get that expansion and place it on your city grid.
If you do have enough coins and it's still greyed out, right click on your screen, select support, then fill out a ticket to get it fixed for you.