I'm in a situation where one person left the company so I will work as his replacement. I am new to the place so I want to tell the client through mail and orally that "I will work instead of / in replacement of XYZ Person". I have found something like "後任". But how do I use this word? Please guide me.
後任 ("successor") refers to a person (i.e., a noun). So the simplest usage of this word is 私は彼の後任です, although this may look a little too blunt. Instead, you can say something like 来月よりXYZさんの後任として勤務致します.
～の代わりに is a very handy set phrase meaning "in place of ～" or "instead of ～", and you can say XYZさんの代わりに勤務致します. But this may imply your predecessor was somehow problematic. If he suddenly left the company and everyone else was annoyed, saying XYZさんの代わりに is natural. Otherwise, probably 後任として is the safer choice.