Many other people have answered, there is no need to pause in that sentence, either before or after the word that, and they are correct.
However, you may of course want to pause in that sentence - perhaps for emphasis, or to catch your breath, or simply to let your listener catch up...
In that case, you should pause before the "that": the word "that" introducing a subordinate clause belongs with the clause it introduces:
I recently realized | that English is so useful but not easy to master.
Putting the pause after "that" would sound a little strange (though often people do pause at that point, usually when they're trying to think of what to say next :)