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Can hair dresser relocate to Canada as a skilled worker

If you have a job offer from an employer in Canada and that employer is able to obtain an approved LMIA, you can then apply for a closed work permit.
 
Secondly, will I be demanded of English proficiency test as a hairdresser?
Thank you

Of course, but I will be much harder to get a work permit. Your future employer needs to prove that no Canadian or permanent resident can do this job (hairdresser).