There is plenty of private work available, and it pays well for language teaching - I know people who are charging QAR200/hour. As for permanent positions, most efl teachers, at least those who have been recruited from abroad, have tonnes of experience and additional specialised EFL/linguistics qualifications such as MA's/Diplomas. You might also consider getting an IELT's testing qualification - the Brit Council run training courses, and then you will find you have a regular supply of work - there is also other testing work you could do.

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