You can try a clean first:
RAILS_ENV=production bundle exec rake assets:clean
RAILS_ENV=production bundle exec rake assets:precompile
Or in one line, as in this migration steps page:
sudo -u git -H bundle exec rake assets:clean assets:precompile cache:clear RAILS_ENV=production
If the issue persists, try to find the missing elements, as in this comment (for gitLab-CI, but the same idea would apply here)
Finally, check if recent versions of GitLab don't need some changes in the NGiNX settings, as in issue 6216, for the assets folder to be accessible.