Is there anyone around today who knows the trop for tehillim, mishlei, iyov etc?
Is there any way to learn it?
There is a book ‘Taamei Hamikra put out by Eshkol that has the visuals and the hierarchy, to figure how phraseology should work ( and to correct the texts that leave out trop but insert errant commas) but as to the sounds, I have yet to find a specimen. the best bet is to find an old sfardi singing tehillim, and to ask him if he know what he is doing.
Rav Levi Sudri has an excellent collection of CD’s, etc… with all of Tanach leined, primarily in Moroccan Sephardi Nusach, but Ashkenazi as well.
There are many people who know Ta’amei Emet well. Just about every sefardi over fifty, and some ashkenazi ba’alei kria. I have mp3s of the ta’amim plus some perakim of tehillim and Eishes Chayil. Kinnor trope trainer software has a program that teaches it. Google them.