Spicy sauce in vessel at university (7)
I believe the answer is:
ketchup
'spicy sauce' is the definition.
(I've seen this before)
'vessel at university' is the wordplay.
'vessel' becomes 'ketch' (ketch is a kind of vessel).
'at university' becomes 'up' ('up' can mean studying at university).
'ketch'+'up'='KETCHUP'
'in' acts as a link.
(Other definitions for ketchup that I've seen before include "Red sauce" , "Spicy tomato sauce" , "Sauce made largely of tomatoes" , "Piquant sauce, often tomato based" , "Thick sauce, with tomatoes" .)