There are many synonyms that can be used instead of "keep under cover." For example, "conceal" means to hide something or keep it secret. "Camouflage" means to disguise something so that it blends in with its surroundings. "Disguise" means to alter the appearance of something so that it is unrecognizable. "Obfuscate" means to confuse or make something unclear. "Mask" means to conceal or hide something by wearing a veil or other covering. "Secure" means to protect something from harm or theft. "Protect" means to keep something safe from danger or harm. "Sequester" means to isolate or separate something from outside influences. All of these words convey the idea of hiding or protecting something.