Go to university with desire for painting (7)
I believe the answer is:
gouache
'for painting' is the definition.
(gouache is a kind of painting)
'go to university with desire' is the wordplay.
'to university' becomes 'u' (abbreviation for university).
'with' means one lot of letters go next to another.
'desire' becomes 'ache' (ache can mean a passionate desire for something).
'go'+'u'+'ache'='GOUACHE'
(Other definitions for gouache that I've seen before include "Watercolour painting with opaque colours" , "Picture" , "Paint medium" , "work" , "Watercolour mixed with gum" .)