Obstinacy namely involves terribly stern caning (13)
I believe the answer is:
intransigence
'obstinacy' is the definition.
(intransigence is a kind of obstinacy)
'namely involves terribly stern caning' is the wordplay.
'namely' becomes 'ie' (short for 'id est', 'that is' in Latin).
'involves' means one lot of letters goes inside another.
'terribly' indicates anagramming the letters.
'stern'+'caning'='sterncaning'
'sterncaning' is an anagram of 'ntransigenc'.
'ie' placed around 'ntransigenc' is 'INTRANSIGENCE'.
(Other definitions for intransigence that I've seen before include "Unwillingness to agree" , "Refusal to change one's views" , "Refusal to budge" , "Obstinacy" , "Stubbornness" .)