An extent of surface; a field of study (4)
I believe the answer is:
area
I believe this is a double definition.
'an extent of surface' is the first definition.
(I've seen this in another clue)
'a field of study' is the second definition.
(I've seen this before)
(Other definitions for area that I've seen before include "Field -- expanse" , "Extent of a 2-dimensional surface" , "Geographical region" , "The measure of a surface" , "Field of activity or surface" .)