Seat advertisement with rigour oddly abandoned (9)
I believe the answer is:
posterior
'seat' is the definition.
(I know that seat can be written as posterior)
'advertisement with rigour oddly abandoned' is the wordplay.
'advertisement' becomes 'poster' (poster is a kind of advertisement).
'with' means one lot of letters go next to another.
'oddly abandoned' indicates alternate letters (letters in odd-numbered positions removed).
The alternating letters of 'rigour' are 'ior'.
'poster'+'ior'='POSTERIOR'
(Other definitions for posterior that I've seen before include "Rear" , "Hindquarters" , "Behind" , "Further back; bottom" , "later" .)