Complex sentence: He moved to be headmaster at Abingdon School (1970--75), Shrewsbury School (1975--80) and Eton College (1980--94) and he was Rector of Lincoln College, Oxford (1994--2000).
Split into simpler sentences: He moved to be headmaster at Abingdon School (1970--75), then Shrewsbury School (1975--80). More recently he was Head Master of Eton College (1980--94) and Rector of Lincoln College, Oxford (1994--2000).