Exceptional students may be able to get fellowships which do not require teaching. Admission to a graduate program is not guaranteed. It depends on appropriate undergraduate preparation and performance. Some graduate programs are much more selective than others. Likewise, a person may be accepted as a master's candidate but not as a doctoral candidate.
Many new careers combine interests, expertise and preparation in two areas.
Forensic science - DNA fingerprinting in criminal cases. Science policy - an interest in the politics of health care and research. Biostatistics - statistical analysis of mortality rates, clinical data and progression of epidemics. Potent law - the legal issues surrounding the patenting of genes, biological reagents, etc. Science journalism - writing about developments in Biology.