If you are looking for a career in patents & intellectual property, there are a good number of graduate schemes to consider. Also, look at pharmaceutical company schemes as there could be opportunities in data science, communications, sales & marketing or medical information. NHS graduate schemes have opportunities in health informatics, too.
Look out for smaller companies, particularly in medical/health communications and data science. They may not have graduate schemes, so it might mean applying for entry level, immediate start positions.
Use our resources for researching science employers to look for opportunities.These may be advertised, or you could try speculative approaches.