Nurtured and dyed outside America (9)
I believe the answer is:
sustained
'nurtured' is the definition.
('sustain' can be a synonym of 'nurture')
'dyed outside america' is the wordplay.
'dyed' becomes 'stained' (staining is a kind of dyeing).
'outside' means one lot of letters goes inside another.
'america' becomes 'us' (abbreviation for the United States).
'stained' going around 'us' is 'SUSTAINED'.
'and' is the link.
(Other definitions for sustained that I've seen before include "Kept (something) going" , "held up" , "suffered" , "prolonged" , "Steadily maintained" .)