There are several synonyms for the phrase "draws up on." Some potential options include "approaches," "pulls up," "arrives at," "reaches," and "comes to a stop." Each of these phrases can be used in a slightly different context to convey a similar meaning. For example, "approaches" might be used when discussing a vehicle that is slowly getting closer to a destination, while "pulls up" might be used when referring to a more sudden stop. Ultimately, the choice of synonym will depend on the specific situation and the speaker's intended tone and meaning.