Some champion traits produce a certain resource per turn, such as Gildar or Research Points. There is now a big focus on making cities amplify resource production instead of creating it. I think that as long as a resource-producing chamption is inside a city, their production should be added to the city's base production and all the modifiers applied to it.
For instance, you have a city with that produces 1 Gildar per turn, with an improvement that boosts Gildar production by 50 percent. Normally, this produces 1.5 Gildar per turn, but if you station a champion with the great merchant trait there, the city should produce 4.5 Gildar per turn.