When will Apple be carrying Games of Thrones, Season 4 episodes?

We are all users here, it will all depend on when the studio supplies the content.

If you research this issue, you'll note that the producers of Game of Thrones have purposesly delayed releasing Game of Thrones new episodes to iTunes in the hopes that people will pirate it. I've read interviews where they have stated that the buzz around the piracy of the show is a huge marketing boon for them.

It's pretty disgusting of HBO to encourage their own show to be pirated in order to get the word out by purposefully delaying release to iTunes.

It was initially delayed because of an exclusivity clause between HBO and Foxtel, but the HBO/Foxtel exclusive rights issue is over and done with already. GOT S4 is available right now for a very, very reasonable price on Google Play - so why not iTunes? I'll wait a short while for Apple to get up to speed, because I would prefer to have all my seasons of GOT available on the same platform. But I won't wait too long for Apple to catch up before I cave & buy the android version of S4 GOT.

Regardless of the absence of any previously enforced agreements with HBO and other entities, the timing of episode posting to iTunes is not Apple's decision, it is up to HBO and the producer/distributor of the show.