President Yukino is from the NTR series of games, and it came out after Treasure Hunter Claire due to Yukino's popularity in TH Claire... at least so I've heard.
Now, the order of the games from the RPG series, of the ones mentioned above, is TH Claire, Collete (you are here), Tear and the Library or Labyrinths. The Yukino game, is, I think, an AU where Yukino never ended up in the TH Claire world, or after she returned from the TH Claire world, or something.
Either way, none of the games are actually directly connected, so what order you play them in doesn't matter. You just have the occasional cameo "from another world" which helps promote the other games. For example the girls from TH Claire show up in the previous game, Demon Queen Melissa, for a bit.