Pig-headed, contrary objections endured (8)
I believe the answer is:
stubborn
'pig-headed' is the definition.
(I've seen this before)
'contrary objections endured' is the wordplay.
'contrary' shows that the letters should be reversed in order.
'objections' becomes 'buts' (I've seen this before).
'endured' becomes 'born' (I am not sure about this - if you are sure you should believe this answer much more).
'buts' backwards is 'stub'.
'stub'+'born'='STUBBORN'
Can you help me to learn more?
(Other definitions for stubborn that I've seen before include "small boat in Loire, good for going around river" , "Unwilling to yield or grant a point" , "Rigid" , "Sticky" , "Obstinate, mulish" .)