Press going after corporate image in stigmatising article (8,4)
I believe the answer is:
branding iron
'stigmatising article' is the definition.
(device for forming a mark or stigma)
'press going after corporate image' is the wordplay.
'press' becomes 'iron' (ironing is a kind of pressing).
'going after' means one lot of letters go next to another.
'corporate image' becomes 'branding'.
'iron' put after 'branding' is 'BRANDING-IRON'.
'in' acts as a link.
(Other definitions for branding iron that I've seen before include "Implement for marking livestock" , "identifies the beast"" .)