Teaching sadly contrived — very put out (8)
I believe the answer is:
doctrine
'teaching' is the definition.
(doctrine is a kind of teaching)
'sadly contrived very put out' is the wordplay.
'sadly' indicates anagramming the letters.
'very' becomes 'v' (common abbreviation).
'put out' is a deletion indicator.
'contrived' with 'v' removed is 'contried'.
'contried' anagrammed gives 'DOCTRINE'.
(Other definitions for doctrine that I've seen before include "In credo" , "On credit (anag.)" , "Article of faith" , "System of beliefs" , "Set of religious principles" .)