Mais adiante, em Capítulo 45 do AFFC ,
Sam Tarly meets a novice named Pate with the same features as Pate from the prologue. Since Jaqen H'ghar is a faceless man, he has presumably assumed Pate's identity, and this is why Pate was killed. Unfortunately as of the end of ADWD we do not know what Jaqen is ultimately trying to accomplish.