Is it possible to work as a translator or interpreter without having a degree or a specialised language qualification (e.g. translation/interpreting diploma)?
It is possible (especially in the case where no high-level preparatory courses and qualifications exist for certain languages), but not necessarily easy. You would generally need to have strong, prior, relevant work experience in translation and interpreting and may be asked to validate your specialist linguistic competencies through tests demanded by potential clients (e.g. translation companies).
