带 here is the verb 'to bear/carry,' so
带伤 literally means 'carrying injury.' It functions adverbially before another verb:
带伤上场 (take the field while hurt),
带伤训练 (train through injury),
带伤完成比赛 (finish the race injured). Same pattern:
带病 (dàibìng, 'while ill'),
带孕 (less common, 'while pregnant').
