University town's giving Bill openings (8)
I believe the answer is:
readings
'bill openings' is the definition.
(initial debates on a bill in parliament)
'university town's' is the wordplay.
'university' becomes 'reading' (I've seen this before).
'town's' becomes 's' (I am not sure about this - if you are sure you should believe this answer much more).
'reading'+'s'='READINGS'
'giving' acts as a link.
Can you help me to learn more?
(Other definitions for readings that I've seen before include "Texts" , "measurements" , "Formal recitals or figures from a meter" .)