I have found that the best way to deal with pull requests that have failed validation due to coding standard error is to close the PR, delete the remote branch in Git and create a new one with the corrected code pushed to it. This is, of course, a bit fiddly and one would rather get the standards right first time. Is this the correct approach? Simply pushing a new commit causes grief in that the local and remote branches are out of sync.
You can add a second commit and push to the same branch, which is what I'd generally do. The PR will be updated with additional commits to the PR's branch.
git add --patch git commit git push REMOTENAME BRANCHNAME
If your branch hasn't been merged (and you're not concerned about others having worked on the same branch), you can also amend your commit and then force-push. But this is more likely to cause grief IMO.
git add --patch git commit --amend git push -f REMOTENAME BRANCHNAME
If you really regret a PR, you can delete the remote branch and start over. This will probably destroy the PR, but you can make as many branches and pull requests as you like.
A colon before the branch name will push "nothing" to that branch, deleting it.
git push REMOTENAME :BRANCHNAME