Yes , you can definitely apply as a private candidate for the CBSE board exam after taking a TC from your school following a failure in the compartment exam.

Students who fail in a CBSE board exam are eligible to reappear as private candidates in the subsequent examination. Obtaining a Transfer Certificate (TC) from your previous school is not a mandatory requirement for appearing as a private candidate. However, it's generally advisable to have it for future reference or admission purposes. You'll need to register directly with the CBSE board as a private candidate, following the prescribed procedure and paying the required fees.

Here are some important points you have to consider :

• Syllabus and Exam Pattern: Ensure you are aware of the syllabus and exam pattern for the year you're appearing.
• Preparation: Plan your studies effectively as you'll be responsible for your entire preparation without the support of a school.
• Exam Centers: Choose an exam center that is convenient for you.
• Admission Process: If you plan to pursue higher studies, having a TC might be beneficial for the admission process.
  
  

I hope this information is helpful to you.