At university old Ruth gets arrogant (6)
I believe the answer is:
uppity
'arrogant' is the definition.
(I've seen this before)
'at university old ruth' is the wordplay.
'at university' becomes 'up' (slang term meaning at university).
'old ruth' becomes 'pity' (synonyms. I am not sure about the 'old' bit.).
'up'+'pity'='UPPITY'
'gets' acts as a link.
Can you help me to learn more?
(Other definitions for uppity that I've seen before include "'Self-important, overweening (6)'" , "Bumptious" , "Cheeky or presumptuous" , "Pert; haughty" , "Informally presumptuous or self-important" .)