Why won't this reaction work?
You are forming the urea because there is always an excess of phenylpiperazine present to react with the carbamoyl chloride you are forming. You need to add the phenylpiperazine to the triphosgene. The paper by Varjosaari et al. [1] has a procedure (described on Organic Chemistry Portal) that should work.

@Mathew Mahindaratne's suggestion will also work:


  Try reversing the order. First, add 1: 1 triphosgene to 4-bromophenol (with stronger base) and then add phenyl piperazine.


References


Varjosaari, S. E.; Suating, P.; Adler, M. J. One-Pot Synthesis of O-Aryl Carbamates. Synthesis 2016, 48 (01), 43–47. https://doi.org/10/gf4wh2.