Is this correct English : "I enclose my CV in respect of a Chinese teaching position." ?
Is there just one position? If so, what I wrote should be correct. If there are several, I would write:
"I hereby apply for a position as a Chinese teacher. Please find enclosed my CV."
You would probably start by saying, "I would like to apply for the position of" or "I hereby apply for the position of." At the end of the e-mail/cover letter, you would write: "Please find attached my CV."