Are there any jobs I can apply for with a Diploma in Heath Science?

For those in the U.S., it's my understanding that a bachelor's (four-year) degree in health science, for instance, more or less acts a starting off point for further education at graduate school in a particular health-related field, such as nursing, occupational therapy (OT), physical therapy (PT), and/or speech-language pathology (SLP), and/or registered dietitian nutritionist (RDN).

If you're in Australia (I'd looked up "health science and diploma"), here is a government career website for those in Australia:

https://joboutlook.gov.au/default.aspx and can click "explore A to Z" to search for whichever careers that piques one's interest and/or type a careers of interest into "search."

Yes. You can get a job. It may not be in the medical profession, but you can get a job.