Beat edges of thinner part of a pound (7)
I believe the answer is:
trounce
'beat' is the definition.
(trouncing is a kind of beating)
'edges of thinner part of a pound' is the wordplay.
'edges of' says to hollow out the word (remove centre letters).
'part of a pound' becomes 'ounce' ('ounce' is part of 'pound').
'thinner' with its middle removed is 'tr'.
'tr'+'ounce'='TROUNCE'
(Other definitions for trounce that I've seen before include "Hammer" , "Beat heavily" , "Beat badly in recount" , "Wallop" , "summons" .)