Dear Jatin,
Sports opens up many career opportunities for young talents in India. To become a sports person, having a talent in the chosen sport is very important. Along with talent, Strong determination and perseverance is needed.

For every sports person, it is a dream to represent their nation at the international level. You can start your career in school and college level and start play at the State level, Regional level and then explores opportunities at national and international levels.

Other than actually being an active sportsman, then other career opportunity are: sport marketing, coaching, athletic administration, sports medicine, sport promotion, sport psychology and so on.

Sports person can be employed in private and public sector. The Indian Government and Armed forces also have special recruitment drives for exceptional sporting talent. You can also set up your own business in manufacturing of sports equipment after gaining experience in this field.

Job Profiles:

Teacher
Biomechanics
Sport psychologist
Sport Journalist
Sports PlayerSports Coach & Instructor
Commentator
Sports Photographer
Personal TrainerProfessional Athlete
Physical Education Teacher
Health Advice Officer
Health & Public Services Leader

Some areas where you can find jobs of sports field are mentioned here:

Media, Sports & Advertising Companies
Sports Management Industry
Educational Institutions & Colleges
Merchandising (Retail) Companies

Top colleges which offers courses in Sports are:

1.Institute Of Sports Science And Technology

offers distance Program In Diploma In Sports Sciences, Diploma In Sports Management, Diploma In Sports And Exercise Psychology, Certificate Course In Sports And Exercise Nutrition, Masters Program In Sports Management.

2. Delhi University, Department Of Sports Science offers

Masters In Physical Education, PhD In Physical Education

3. Lovely Professional Universityoffers

Bachelor of Physical Education & Sports (BPES), BSc. (Health and Physical Education), B. P. Ed, M. P. Ed , Ph. D.

4. University of Mysore

Bachelors In Physical Education, Masters In Physical Education,

5. University of Punjab: M. Sc. In Sports Science, M. Phil In Sports Science.

6. School Of Allied Health Sciences Manipal University: M. Sc. In Exercise And Sports Science.

Some other Colleges in India offer study in Sports:

National Institute of Sports, Patiala
Indira Gandhi Institute of Physical Education and Sports Sciences, New Delhi
Lakshmibai National Institute of Physical Education, Gwalior
Lakshmibai National College for Physical Education, Thiruvananthapuram
Tata Football Academy, Jamshedpur
National Cricket Academy, Bangalore
Delhi University
Hope this helps.

Good luck!