Reading through the books I to V, I couldn't a real explanation about the tripartite of the soul as I could find in the Phaedo. Reading in some analysis of the books[1], and the wikipedia article about it[2] sounds like the definition of the 3 parts are described through the book IV, however reading and listening the audibook from the book IV, is hard to pin-point where exactly those points are defined.
References:
[1] https://plato.stanford.edu/entries/plato-ethics-politics/
[2] https://en.wikipedia.org/wiki/Plato%27s_theory_of_soul#The_tripartite_soul