Unfortunately The Quiet Man is not currently scheduled for a Blu-ray release.
I believe it would need restoration. The elements exist. It's only a matter of money and time.
It needs a lot of restoration as I don't think it was graded properly by Republic when it was first released and any subsequent releases on film, video or DVD have not been without their faults.
It would be great if someone or an organisation took the task on as it would be a shame to lose this classic to future generations.
I believe that The Quiet Man was the best selling video in the UK when it was first released so a restored DVD release could be a money winner.