How can you make yourself more desirable to employers when you may not have the preferred experience they are asking for?

As the title says, I am trying to apply for different jobs than what I have been doing the past 6-7 years. I bring a lot to any team and would be a good employee to have but I often feel overlooked because my past work experience doesn't really match up with what I'm applying for. Is a really good cover letter the answer here, or do employers even take the time to read those with all the applications they see?

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