Rival has inn improved, but it's cosmetic (4,7)
I believe the answer is:
nail varnish
'it's cosmetic' is the definition.
(nail varnish is a kind of cosmetic)
'rival has inn improved' is the wordplay.
'improved' indicates anagramming the letters.
'rival'+'has'+'inn'='rivalhasinn'
'rivalhasinn' anagrammed gives 'NAIL-VARNISH'.
'but' acts as a link.
(Other definitions for nail varnish that I've seen before include "Manicurist's cosmetic lacquer" , "Substance applied to finger ends" , "Make-up for fingers and toes" , "Lacquer applied to the body's extremities" , "Shiny fluid applied to the tips of one's digits" .)