Given that there is only one major railway heading into Trieste as the line trundles along from Venice, and given that the small number of branch lines heading out of the city only have very limited service, Trieste is the sort of destination that naturally leans towards getting a hire car.
Note that the chances are that if you are flying into Trieste, you might also be looking at driving into neighbouring Slovenia and Croatia, especially to visit some of the coastal cities around Pula and Rijeka.
Most Trieste car hire offices will be quite happy allowing you to drive out of Italy, but they may only offer a limited backup service. Always check with your insurance before driving a hire car across any border, even within the European Union.
Should you rent a car in Trieste? Yes