Old, fat and pompous (7)
I believe the answer is:
orotund
'pompous' is the definition.
(I've seen this before)
'old fat' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'fat' becomes 'rotund' (I can't justify this - if you can you should believe this answer much more).
'o'+'rotund'='OROTUND'
'and' acts as a link.
Can you help me to learn more?
(Other definitions for orotund that I've seen before include "Full, clear and musical" , "Bombastic" , "Not dour (anag.)" , "booming" , "Loud or pompous" .)