Bill Gates' centre parting a puzzle (6)
I believe the answer is:
poster
'bill' is the definition.
('poster' can be a synonym of 'bill')
'gates' centre parting a puzzle' is the wordplay.
'gates' centre' becomes 't' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'parting' is an insertion indicator.
'a puzzle' becomes 'poser' (I've seen this before).
't' placed inside 'poser' is 'POSTER'.
Can you help me to learn more?
(Other definitions for poster that I've seen before include "bulletin board participant" , "Printed advert" , "Largfe public notice." , "surfer who leaves messages on boards?" , "Large sheet of paper advertising something" .)