If you have sent your CV in and are waiting for a response from a company, please remember that not all companies will get back to you with an acknowledgement from just sending in a CV.
Check that if you are applying for a specific position that the end date has finished before sending any kind of follow up letter as any employer has to let the end date run before finalising contact with people.
Remember to write your letter going through the relevant skills to the role that you are applying for that are connected to what the company is looking for. You need to be able to give them a snapshot of what you can do for them should you join them.
If you are looking at how best to write your covering letter, please see the below example which you can use as a guide.
Example Follow-Up Letter After Submitting a CV
222 Every Road, Any Town, AA1 1BB
Mrs Jane Smith
Application for the role of XXXX
I recently submitted my CV as I am interested in applying for the position of XXX that you have got advertised and I wanted to ensure that you had received my application and to see if you needed any further information from me with regards to this role.
SHORT SUMMARY ABOUT YOUR SKILLS and what you can bring to that company and how your skills are relevant to the position they are looking to recruit for. Follow the job description and make short explanations about what you can do and how this is relevant and would be beneficial to them. Try and sell your skills on paper e.g.: having done X,y, z I now have the experience to do x,y and z.
I am very eager and enthusiastic to talk to you further about this position and would be available for an interview at your convenience should you be interested in my skills further.
May I take this opportunity to thank you for reading my application and I hope to hear from you in due course. You may contact me on TELEPHONE NUMBER and or EMAIL.
I look forward to hearing from you.