Applicant can apply for E-7 visa when the applicant is hired by Korean public or private company. There are 82 job types (occupations) and you can look at the source from Livinko below.
Updated on April 06, 2017: There are 84 occupations for E-7 visa.
It is very important that the applicant is hired for the occupation in the list of job types (occupations) for E-7. Some immigration officers will help you to choose the right occupation which matches with your case. However, many officers will request you to choose one from the list. Then they will just review the documents according to the occupation you indicated.
The immigration office and ministry of justice will investigate the current level of demands on foreign professional workers of new occupational fields. They will select occupations taking accounts of effects, substitutability of Korean citizens and other general criteria. When they research on demand, they will consider education level, work experiences and employment conditions of each occupational type.
Specific code number will be given to a specific occupational type in order to make it possible to analyze, manage, and calculate statistics of the current state of affairs, numbers, and types of jobs that are introduced. Occupation code number will be given in a form of Arabic numerals of small type in accordance with Korea’s standard job classification.
The immigration office will closely examine whether the applicant satisfies requirements for the most similar occupation types, necessity of the job introduction, and substitutability of Korean citizens. After rigorous review, they will only allow occupations that are most reasonable to introduce.