Pretext contributing to extensive ill-feeling (4)
I believe the answer is:
veil
'pretext' is the definition.
(veil can mean a pretext or facade)
'contributing to extensive ill-feeling' is the wordplay.
'contributing to' says the answer is hidden in the clue.
'VEIL' can be found hidden inside 'extensive ill feeling'.
(Other definitions for veil that I've seen before include "Yashmak, for instance" , "Yashmak, e.g." , "coverage" , "Face concealer" , "Cover, conceal" .)