Being a Zoology graduate, this question came to my mind for several times before I decided to come to this field. So, I feel I can share my experience with you that I have gained yet.
Zoology in itself is a very vast subject dealing with various major aspects of Biology like Biotechnology, Bioinformatics, Wildlife Science, Biochemistry, Ecology, Cell Biology, Applied Zoology, Immunology, Parasitology, Genetics, Endocrinology, Animal Physiology etc. You'll cover the basics of all these sub-groups during your bachelor's. Infact, present day specialization courses like Fishery, Sericulture, Apiculture and others are all derived from this mainstream subject. You can do specialization in any of them from a recognized college or university after getting your degree. During your M.Sc., you can also apply for fellowship programmes like PMRF etc. and gain the experience of working under renowned scientists along with certain fellowship amount based on your project abstract.
Completion of your undergraduate course followed by post graduation will open up a wide range of career opportunities for you in different sectors. If you work hard in your MSc then you will also be able to clear CSIR - NET (LS) or NET (JRF) or you can also clear GATE (Evolution or Ecology) or UGC NET (Environmental Science), which will make you eligible for Lecturership, may provide you research fellowship or even assure a post in government institutes as a professor. Teaching in state government schools or KVs is also an option for you, after doing M.Sc., followed by B.Ed. or vice versa.
If you don't want to continue your higher education after completing your B.Sc. in Zoology, you can also sit for various competitive exams of Civil Services, Banking, Railways etc. If you have interest in business, you can also go for your own small-scale Apiculture, Sericulture or Fishery, employing the knowledge you have gained. MBA can also be done.
You can also appear in exams conducted by ZSI (Zoological Survey of India) or IFS (Indian Forest Service) or state level forestry exams for getting a government job in this field.
It is one of the most preferred courses of NEET aspirants. So, if you are also a NEET aspirant, you can join this course to remain in constant touch with Biology-the subject with highest weightage in that exam. In addition to it, you can join some online courses available for NEET to boost up your preparation. And keep revising the entire syllabus of class 11th and 12th Physics and Chemistry in your spare time along with practicing the previous year question papers. You will get enough time for your NEET preparation as the schedule for the 1st and 2nd semesters are usually not very hectic. But right before your End-semester exams, you'll also have to focus a little on your degree exams, as you wouldn't like to score below average in them.
Try to keep your graduation % above 60 in order to keep your options open for later on as a back up plan.
Don't hesitate to ask if you have any more queries.
I hope this answer will be helpful to you.
Best wishes for the future!
You can get jobs in various Government sectors after your Graduation. But mostly people tends to go for Masters and after that clearing the CSIR NET or GATE with Evolution and Ecology Paper.
You can choose any specialization course in genetics, biotechnology, Endocrinology, Immunology, applied zoology, wildlife science, Ecology and you will be eligible for all these specialized courses in most university.