There is no age limit to apply for EU careers and jobs. The maximum age, however, is determined by the retirement limits provided by the Staff Regulations of EU officials, which is 66 years (or in some special cases and on an individual basis, even before that). The minimum age is not determined either given the fact that to meet the formal criteria, candidates are certain to be at least 18 years old.
See also:
Eligibility Criteria | Staff Regulations
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