There will be multiple answers to this question, as different individuals will have divergent approaches to the issue of economy. I would say that an emerging sector of the Indian economy would be energy development and the realization of energy alternatives. India is a nation that is consuming a great deal of energy, such as traditional oil and burning of fossil fuels for factories. I think as the demand, both in India and worldwide, increases, there will be a need to explore energy alternatives such as solar, biofuel, and wind energy, where sector emergence could transpire. The growing demand for products from abroad might create the import/ export sector as one of growth. Certainly, Information Technology as well as telecommunications represent growth sectors in the economic structure, and there is little reason to believe that these domains will not continue their increase. Additionally, real estate development and speculation might experience growth because of the population demands and the need for more property development in cities. Since a large portion of India is rural, agriculture should continue to be a growth industry, and if more innovations in research can reach these areas, growth in farming and agriculture can constitute a growth sector.
My concept of what is an emerging sector is somewhat different from the one implicit in the answer above. I see emerging sector as one which ahas begun do develop only recently, and therefore is not really that well developed, but is likely to develop and grow fast in future. Many of the sectors identified by akannan in the post above - such as information technology, communication and agriculture - are already well developed and therefore do not qualify as emerging sector.
As it appears to me some emerging sectors in Indian economy are medical treatment, medical research, and knowledge process outsourcing. Like information technology, india is becoming a very competitive source for providing such services to many developed countries around the world.