Keeping locked up refers to the act of securing or confining something within a certain space or location. There are several synonyms that can be used in place of this phrase, depending on the context of the situation. For instance, words such as imprisonment, incarceration, and detention can be used to refer to the confinement of individuals within a prison or detention facility. Meanwhile, phrases such as keeping under lock and key, locking away, and securing can be used to refer to the general act of locking up valuable items, documents, or other personal belongings. Other options can include terms like confining, restraining, or even restricting depending on the specific connotation desired.