Please carry on using your computer until a replacement arrives
質問者様の言いたいことは「Please carry on using your computer until a replacement arrives」ですが、これだけですと、恐らく「なんでだ!」と言う苦情が来るので、以下をお勧めします:
「We tried to get replacement computers but none are immediately available. In the meantime, I am sorry but please carry on using your computer until a replacement arrives」。
"In the meantime"は、「それまでは」に当たります。