So I need remove video and then re-apply?Using the copyright material your the video is what's preventing you from getting partnership, so as long as that video is on your channel (whether it's private or not), I would imagine it still counts. Though I'm sure someone else who has come across this issue could tell you more about it.
Partnership support said " Once your account has this material removed (copyright content), please email us at onboarding {at} network {dot}com so we can continue the partnership process."Chances are that you probably have to delete the video from your channel. But wait for another response before you do, because I may be wrong. Isn't there a period of time before you can apply again for partnership after given a copyright claim?