Touching line from Brown, respected chap (7)
I believe the answer is:
tangent
'touching line' is the definition.
(a line touching a circle)
'brown respected chap' is the wordplay.
'brown' becomes 'tan' (tan is a kind of brown).
'respected chap' becomes 'gent' (gentleman).
'tan'+'gent'='TANGENT'
'from' acts as a link.
(Other definitions for tangent that I've seen before include "Line touching circumference" , "mathematician's line" , "Trig ratio" , "Line that touches curve without crossing it" , "Geometric line" .)