Does sincere repentance and remorse guarantee concealment from disgrace in this world, and is there a specific supplication for concealment?

You should offer sincere repentance purely for the sake of Allah the Almighty, not out of fear of scandal. If your repentance is true, have a good opinion of Allah and strive in supplication for concealment (of your sins) and well-being, for He is as His servant expects Him to be. It is hoped that He will conceal your sins and grant you well-being. If you are afflicted with a trial, be patient and consider it an expiation and an increase in reward. There is no specific supplication for concealment, but strive in supplication, draw closer to Allah, and ask Him of His bounty.