A wood on the borders of a local river (7)
I believe the answer is:
spinney
'a wood' is the definition.
(I have seen 'little wood' mean 'spinney' so perhaps 'wood' could also mean 'spinney')
'on the borders of a local river' is the wordplay.
'on' means one lot of letters goes inside another (as in clothing 'on' a person).
'the borders of' says to hollow out the word (remove centre letters).
'a local' becomes 'native' (relating to a particular area).
'river' becomes 'spiny' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'native' with its centre taken out is 'ne'.
'ne' going inside 'spiny' is 'SPINNEY'.
Can you help me to learn more?
(Other definitions for spinney that I've seen before include "Small clump of trees" , "little wood" , "Small area of trees" , "Copse of trees" , "Cops, we hear" .)