You appear to be the Respondent in the case.
It is the duty of the Petitioner (and NOT of the Respondent) to remove the defects of filing in the Supreme Court registry. If the petitioner does not take appropriate steps, his SLP may get dismissed.
If the high court judgment is in your favour, and if sufficient time has passed, you can file a contempt petition in the high court if the order in your favour has not been implemented. Once you do that, the petitioner will rush to remove the defect in SC and will try to get a stay order from the SC.
Meanwhile, you can also file a caveat in the Supreme Court, if you so like, which will ensure that you are heard by the Supreme Court before any interim order (such as a stay order) is passed by the Supreme Court in the above SLP.
Dr. Ashok Dhamija is a New Delhi based Supreme Court Advocate and author of law books. Read more about him by clicking here. List of his Forum Replies. List of his other articles. List of his Quora Answers. List of his YouTube Videos.