Yes, you can register for the UGC NET Exam with a gap year after post-graduation. Here are the detailed steps and requirements for the registration process:

Eligibility Criteria:
To be eligible for the UGC NET Exam, you must fulfill the following criteria:
1. You should have completed a post-graduation degree from a recognized university with at least 55% marks (50% for candidates from reserved categories).
2. The age limit for the exam varies depending on the category. For general candidates, the maximum age limit is 30 years. However, there is a relaxation of 5 years for candidates belonging to OBC, SC, ST, and PwD categories.

Registration Process:
To register for the UGC NET Exam, you need to follow these steps:
1. Visit the official website of the National Testing Agency (NTA), which is the conducting body for the UGC NET Exam.
2. Look for the "UGC NET" section on the website and click on it.
3. Read the instructions and eligibility criteria carefully before proceeding.
4. Click on the "Apply Online" link and fill in the required details such as personal information, educational qualifications, and contact details.
5. Upload scanned copies of your photograph and signature as per the specified format and size.
6. Pay the application fee through the available online payment options.
7. Review all the details provided and submit the application form.

Documents Required:
During the registration process, you will need to upload the following documents:
1. Recent passport-size photograph.
2. Scanned signature.
3. Category certificate (if applicable).
4. PwD certificate (if applicable).
5. Post-graduation mark sheet and degree certificate.

Important Dates:
It is crucial to keep track of the important dates related to the UGC NET Exam. The application process usually starts a few months before the exam date. You can find the detailed schedule on the official NTA website.

Preparation:
While registering for the exam is an important step, it is equally essential to prepare well for the UGC NET. Make a study plan, refer to reliable study materials, solve previous years' question papers, and consider joining online or offline coaching institutes for guidance.

In conclusion, with the gap year after post-graduation, you can definitely register for the UGC NET Exam. Just ensure that you meet the eligibility criteria, complete the registration process accurately, and prepare effectively for the exam to increase your chances of success.