I used to be on recruitment panels a lot in the NHS for IT/Digital. We used to score the applications against the Person Specification. If you did not mention somewhere all of the essential criteria and you meet them ( or could easily meet them), you would not be shortlisted. If a lot of people had the essential criteria then we would take the top 6 applicants or so, based also on desirable criteria as well.
People marking the applications don't always understand the skills its takes to do a role in another organisation, so you need to be very clear what your skills and experience are, as relevant to the post you are applying for. No point being, for example an excellent programmer for a job in networking etc . Lots of It people don't understand this and have CVs/applications that are full or jargon but don't explain how you are the right person for this particular job. Be clear and succinct, be focussed on how you meet the job spec. Don't go into massive detail about the stuff that is not relevant.
Also remember that people are looking for a good fit for their teams. Show examples of how how you have communicated effectively at lot of levels, have worked well in a team and solved problems, ideally working in collaboration with others, as well as on your own. Don't ever be critical of other teams/ organisations/ or managers, or make it sound like everyone else was useless, as it makes you look like trouble ( it's amazing how often i have seen this hero complex). Organisations prefer people who prevent problems, and recognise others contributions.
Make it easy to read: remember people are ploughing through loads of these. Use plain English - your goal is to be understood and communicate clearly. Simple language is better than flowery text. .Use a clear font, in one size; use underline or bold, not both. Left justify. No pictures, or icons.
good luck!