Laurence was born in Egypt to Alfred Joseph Clancy and Agnes Hunter.
In 1951 University of Liverpool conferred the bachelor of science (honours) degree.
Clancy qualified as an Education Officer with the RAF and began teaching at Royal Airforce College Cranwell.
Laurence assembled a book manuscript from his lectures. In 1975 John Wiley & Sons and Pitman issued his textbook Aerodynamics. It was re-issued in 1978 by Wiley, and in 1986 by Longman. A book review in Journal of Fluid Mechanics described the book as follows:
- The scope of the book is wide and includes the mechanics of flight and aircraft performance in addition to the usual topics of basic fluid mechanics, aerofoil and wing theory, boundary layer theory, gas dynamics and experimental techniques.
- The true aerodynamicist … must combine [mathematics and experiment], using analysis to deepen and extend his knowledge, but continually experimenting in order to check the validity of his assumptions and to improve his understanding of the physical problem. (page xviii)
Reviewer M.W. for Flight International wrote, "The author has a lucid style and puts across a traditionally difficult subject in such a way that the less prepared reader is able to follow the arguments of even the knottiest topics."