PostgreSQL is the program where PokerTracker 4 stores your poker data and if you have deleted it then PokerTracker 4 will be unable to start. To reinstall PostgreSQL you can follow
this tutorial and then manually download and install PostgreSQL v9.3 available
from here. Using a Mac administrator account or administrative privileges install that PostgreSQL and for the password boxes use "dbpass" (no quotes) which is what PokerTracker 4 uses by default. Once PostgreSQL installs successfully reboot your computer and then try starting PokerTracker 4 again.