新しい先生は「New teacher」です。
質問者様のシチュエーションだと。。「I spent a lot of time training the new teacher up only for him/her to leave without saying anything.」
ここの「only for」は、残念なことの展開を示す時に使います。
例えば："I worked hard only for the money to be taken by the taxman"
That teacher is a new hire and I am training him.
I will be helping to train the new teacher.
They hired a new teacher for me to train.
The old teacher left without notice so I will have to train a new one.
The new teacher is replacing the old one that left without notice.
I was surprised that the old teacher left so suddenly but I am getting a new hire.
That teacher is a new hire and I am training him.
（あの先生は新任です、私が指導しています）
I will be helping to train the new teacher.
（私は新しい先生を指導するのを手伝います）
They hired a new teacher for me to train.
（新しい先生が入って、私が指導することになっています）
The old teacher left without notice so I will have to train a new one.
（元いた先生が突然辞めてしまったので、新しい先生を指導しないといけません）
The new teacher is replacing the old one that left without notice.
（新しい先生は元いた先生が突然辞めてしまったのでその代わりに入ります）
I was surprised that the old teacher left so suddenly but I am getting a new hire.
（元いた先生が突然辞めてしまったときは驚きましたが、また新しい先生が入ります）
"New teacher" and "new member of staff"
These are the terms used to describe a 'New teacher', someone who is new in a school,college or university, 'teacher' can also be called a professor, but usually in universities and colleges.
'Member' is to be apart of something, in this context the teaching staff.
"New teacher" と "new member of staff"は、学校、大学などの新任の先生のことを表します。'teacher'（先生）は professor（教授）ということもできますが、たいてい大学や短大の先生のことを指します。
'Member' は、何かのメンバーになること、この場合先生のことを指します。
The teacher that just started working at the school.
The newly hired teacher.
These sentences all speak of a new teacher at a school.
We can use the above to say that a teacher is new and has just started working at a school.
"She is a new teacher, I haven't seen her before."
"She is a newly hired teacher."
"She just started working at the school, she's a new teacher."
これらの表現は全て新任の先生のことを伝えています。これらは、先生が新しく、学校で働き始めたばかりであるということです。
"She is a new teacher, I haven't seen her before."
（彼女は新任の先生だ。今まで見たことがない。）
"She is a newly hired teacher."
（彼女は新任の先生だ。）
"She just started working at the school, she's a new teacher."
（彼女はその学校で働き始めたばかりの新しい先生だ。）
"New Teacher"
This is what you would formally call a new teacher. In the US there is no other one of saying this. However, there are many ways of saying in an informal way.
"Rookie Teacher"
This is one of the informal ways of describing a new teacher even if its a teacher that has many years of experience, they are considered rookies or beginners because they do not know the school system and have to learn it.
"New Teacher"
これは、新任の先生のかしこまった言い方です。アメリカでは、これ以外に言い方がありませんが、くだけた表現ならたくさんあります。
"Rookie Teacher"
これは、その先生が何年もの経験があったとしても新任の先生のことを表すカジュアルな言い方のっ1つです。その学校のシステムを知らなかったり、学ばなければならないことがあるので新人とみなされます。
When a new teacher is appointed it would depend on a number of things as to how you would address them. These things would depend on what is the culture and where the teacher is, is it a formal or informal setting what are the other teachers called? Informally you could address a teacher as Teacher Rose etc, or in more formal settings/structures, mam is commonly used. The teacher however could be asked how she would like to be addressed maybe they would like to be called by their first names or maybe they would prefer being called Mr/Mrs ...... dependent on culture,society and setting.
イギリス 
アメリカ合衆国 
南アフリカ 
アイルランド 
