in particular, if the distance is more than about 1 fm?
At about 1 fm separation the strong force will resist the separation of the quark-antiquark pair any further and create a new quark-antiquark pair between the two. Now you have 2 quark-antiquark pairs using on quark from the newly created pair on each one, shortening the separation once more.
This is a pretty good link of more or less exactly your question.
Hope that helps, and welcome to SE