There are a number of different synonyms available for the phrase "have hold up on," each of which can be useful in slightly different situations. Some common alternatives might include "delay," "postpone," "reschedule," "defer," or "put off." Other options might include "hold back," "wait on," "pause," or "suspend." Depending on the context and the specific needs of the situation, any one of these synonyms might be more appropriate or effective than the others. Ultimately, choosing the right synonym will involve considering the nuances of the situation and determining which phrase will best convey the intended meaning.