Carry on, though stigma envelops America (7)
I believe the answer is:
sustain
'carry on' is the definition.
(sustaining is a kind of carrying on)
'stigma envelops america' is the wordplay.
'stigma' becomes 'stain' ('stain' can be a synonym of 'stigma').
'envelops' is an insertion indicator (I've seen this in other clues).
'america' becomes 'us' (abbreviation for the United States).
'stain' placed around 'us' is 'SUSTAIN'.
'though' is the link.
(Other definitions for sustain that I've seen before include "Keep up; hold for a long time" , "Keep (something) going" , "Nurture, uphold" , "Uphold, strengthen" , "Strengthen; suffer" .)