The need for a TESOL certification
is generally at the discretion of the employer. If your degree is already in a linguistics or educational field, and/or you have a state teachers' licence (or something like a British PGCE), and/or significant
teaching experience in a related field and can provide references, an employer might not insist on a TESOL cert. Normally the requirement will be mentioned in the job ad. However, schools are notorious for poorly composed job ads and the best job ads are often written by professional
You may possibly find it to be much less productive to send resumés/CVs to schools and other potential employers who are not currently advertising any vacancies.
Do check out our job application tips
, particularly item 5.
Do note however, that the governments of most countries nowadays insist on a bachelor degree (often in any subject) for legal employment which usually means obtaining a visa and a work permit.
Hope this helps.