Swear that sulphur is included in the remedy (5)
I believe the answer is:
curse
'swear' is the definition.
('curse' can be a synonym of 'swear')
'sulphur is included in the remedy' is the wordplay.
'sulphur' becomes 's' ('S' can be a synonym of 'sulphur').
'is included in' is an insertion indicator.
'the remedy' becomes 'cure' ('cure' can be a synonym of 'remedy').
's' placed into 'cure' is 'CURSE'.
'that' acts as a link.
(Other definitions for curse that I've seen before include "Invoke evil upon" , "Oath or a call for evil to come upon person" , "Blasphemy" , "Execrate" , "Malediction or expletive" .)