When it comes to securing or protecting something, there are several synonyms for the phrase "placing under wrap." One common term is simply "wrapping," which encompasses the act of enclosing an object with a covering material like plastic, paper, or cloth. Another option is "enveloping," which suggests a more thorough or complete coverage. "Encasing," "covering," and "shielding" are also good options, emphasizing the idea of providing a barrier against outside elements. Similarly, "concealing" and "hiding" convey the sense of keeping something out of sight or preventing it from being discovered. Ultimately, the best synonym for "placing under wrap" will depend on the context and purpose of the action.