Our vet is upset, becoming glassy (8)
I believe the answer is:
vitreous
'glassy' is the definition.
(I know that glassy can be written as vitreous)
'our vet is upset' is the wordplay.
'upset' is an anagram indicator.
'our'+'vet'+'is'='ourvetis'
'ourvetis' anagrammed gives 'VITREOUS'.
'becoming' acts as a link.
(Other definitions for vitreous that I've seen before include "Made of glass" , "Glassy" , "How glaze appears" , "Resembling glass - over suit (anag)" , "Like glass" .)