Internal transfer

Are you asking can you transfer within your department or to another department without going through mobility and an open competition? Are you a CO, EO or HEO?

If you're happy in your org and location, then you should just have a chat with HR and/or managers to ask for a move. Of course, whether or not you talk to your managers may depend on your relationship with them.

Something I've also seen done in the past is to put it in your PMDS with a note that it's for career progression, but that was generally when a person wanted to move to a particular team.

This is really at the discretion of HR and can be quite difficult to achieve. Speaking from experience I found that several divisions fight to retain and keep staff in particular roles within the department and can be quite difficult to get a move or to get them to release you. Your argument might be stronger if there is a health issue involved, I have seen many people get moved/transferred for this reason. Your argument to justify a move to another role will be quite weak if you simply state that you don’t like the role. I would advise to write an email to HR requesting a transfer internally, outline the reasons why, outline your skills/experience and finish by saying you would be grateful if they would consider your request. You have nothing to lose but it will be difficult.