As far as I remember from the anime series and the games, after beating one of eight Gym Leaders in a region, some leader said something about the next Gym Leader.
Like they know who, where, or what specialist-type the next Gym Leader is.
But, I watched the current XY series, Clemont, the Gym Leader of Lumiose City's Gym who travels with Ash, always wonders about the kind of next Gym Leader that Ash will face.
UPDATE
Each region has 8 Gym Leaders, and they give a badge after being defeated. We need all 8 badges to enter the Pokemon League to beat the Elite Four and the Champion.
I just want to know if they, as Gym Leaders, must have known each other or not?