Slight advantages on a hill, in battle (4)
I believe the answer is:
edge
This might be a double definition.
'slight advantages' is the first definition.
Both the definition and answer are adjectives. Perhaps you can see a link between them that I can't see?
'hill in battle' is the second definition.
The definition and answer can be both man-made objects as well as being singular nouns.
Perhaps you can see an association between them that I can't see?
'on a' is the link.
Can you help me to learn more?
(Other definitions for edge that I've seen before include "Upper hand" , "Border, fringe" , "Move furtively; intense quality" , "Advantage (informal)" , "Hem" .)