"Keep under wraps" is a common idiom that means to keep something secret or hidden from public knowledge. To convey the same meaning, one can use a variety of synonyms such as conceal, hide, keep quiet, hush up, keep a lid on, keep mum, suppress, cover up, cloak, shroud, veil, bury, or tuck away. All these phrases essentially mean to protect information or secrets from being revealed or exposed to the public. Whether it's a personal matter or a sensitive business deal, keeping something under wraps can be necessary to ensure confidentiality and avoid unwanted consequences.