Just like other industries, you aim to get better search engine rank results by practicing SEO. On top of the list is creating unique, quality engaging content relevant to the industry. In the case of healthcare, you have to think in terms of popular topics searched by your target users in the internet like medical conditions, symptoms, treatments, specialists, etc. and write articles, create videos, patient testimonials, medical breakthroughs, seminars, information drive, etc. which may interest your market. Quality backlinks and endorsements are very helpful in providing credence to your site. More visitors to your post increase your chance of getting more leads or followers and eventually patrons of your services.
Healthcare is an area that is absolutely dominated by existing and pretty much unassailable high-authority sites: hospitals, universities, charities and other non-profits, journals and established encyclopedia sites like WebMD. It is also an area with very specific legal requirements at least in the Untied States. The first rule of healthcare SEO is don't compete with the behemoths, you aren't going to win. You need a subject or angle that is unsuitable for that kind of authoritative site. Pick your battles.
First of all find your niche like in Which sector of health care you serve like, Dental, physiatrist and according to them find your competitor and research on them. Then find your service keyword and according to them do seo.
I'm not an expert at this question, but I suppose that it would be great to develop the sphere of healthcare. Nowadays medicine is pretty expensive, to my mind and it would be cool to create something free. I heard about a pretty famous company https://inoxoft.com/industries/healthcare/ that could make qualitative software. Of course, it is needed to allot a huge sum from the budget.