Hey Ayushi!

Yes, you can definitely apply for CBSE class 11th after 10th class with a year delay. There are many students who get admitted in 11th class after a year gap due to several reasons. Although not every school allow such students, but there are plenty that do. At the time of admission, you may be asked about the reason of gap. So, be prepared to answer it and at the time of admission make sure you are ready with all the documents like your 10th certificates.

All the best!