I didn't know promotion can appeal like appeal for grades sia

I disagree. HR shortlists all staff eligible to be promoted at ranking meetings around Nov-Jan every year, so there is no need for individual bosses to "put up for promotion". Likely, you were either: 1) Shot down by your own boss or 2) Shot down by other bosses at not defended by your bosses.

It is useless to appeal since there is either: 1) Management actively blocking you or 2) Management unfeeling to defend you. The reason appeals rarely succeed is because your bosses will have to admit that they made a mistake; and it's far more beneficial for them to remain adamant that you don't deserve it.

My advice is to look for a new job (just get out of your agency; other public agencies are fine since it's a boss issue), but can try talking to HR anyway since you have nothing to lose if you are going to quit anyway - not to appeal for a promotion, but to find out what happened so can avoid a similar situation at the next job.