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Longman Dictionary of Contemporary English
further education
noun
EXAMPLES FROM CORPUS
▪ Encourage Ongoing Learning All students should be prepared to pursue further education and training beyond high school.
▪ How can further education help in economic development? 2.
▪ More than 80 percent. of those on youth training gain a qualification or a job, or enter a further education course.
▪ Out of seventy children in the village school only sixteen could go on to further education after the age of ten or eleven.
▪ Some one pointed out that there was no adult institute for further education in Northern Ireland.
▪ Surely, further education could not be so different?
▪ The position of the two sexes has been the exact opposite in relation to further education, and to teacher training.
▪ Thereafter, only a minority proceed to institutions of further education and but a small percentage enter university.
Wiktionary
further education

n. (context UK English) education beyond compulsory schooling, not including university-based higher education.

Wikipedia
Further education

Further education (often abbreviated FE) in the United Kingdom and Ireland, similar to continuing education in the United States, is a term used to refer to education (in addition to that received at secondary school), that is distinct from the higher education offered in universities. It may be at any level above compulsory secondary education, from basic skills training to higher vocational qualifications such as PGCE, NVQ, City and Guilds, BTEC, HNC, HND or Foundation Degree.

A distinction is usually made between FE and higher education (HE), an education at a higher level than secondary school, usually provided in distinct institutions such as universities. FE in the United Kingdom is usually a means to attain an intermediate or follow up qualification necessary to attend university, or begin a specific career path, e.g. Quantity Surveyor, Town Planner or Veterinary Surgeon, for anyone over 16, primarily available at Colleges of Further Education, work-based learning, or adult and community learning institutions.