Cross, head delivering corporal punishment (8)
I believe the answer is:
spanking
'corporal punishment' is the definition.
(thesaurus)
'cross head' is the wordplay.
'cross' becomes 'span' (synonyms).
'head' becomes 'king'.
'span'+'king'='SPANKING'
'delivering' acts as a link.
(Other definitions for spanking that I've seen before include "procedure for maintaining discipline!" , "Hiding" , "Outstanding - traditional punishment for children?" , "Very large" , "Quick and energetic (1)" .)