Such matches have very pointed rivalry (6)
I believe the answer is:
needle
'such matches' is the definition.
The definition and answer can be both man-made objects as well as being singular nouns.
Perhaps you can see a link between them that I can't see?
'have very pointed rivalry' is the wordplay.
'have' becomes 'need' (synonyms).
'very pointed rivalry' becomes 'le' (I can't justify this - if you can you should believe this answer much more).
'need'+'le'='NEEDLE'
Can you help me to learn more?
(Other definitions for needle that I've seen before include "Gramophone record stylus" , "has only one eye" , "Sewing item" , "pinnacle of rock" , "Compass pointer" .)