In this article, we describe how to write a cover letter for an unadvertised job and provide a template and an example for guidance. Dear Ms. Johnson: I am very interested in applying for a management trainee position.How to write a cover letter for an unadvertised job, plus sample application letters for jobs that aren't listed on an employer's website. Need to write a short cover letter to complete your job application? Check out our short cover letter examples and tips in this article! The purpose of a cover letter is to introduce yourself and to demonstrate the fit between your background and the advertised position. Use these sample cover letters if: you're looking for work with a particular employer; there are no advertised vacancies at that employer.