Yes, you need to push process, which means either longer developing time, or higher temperature (eg 27 deg instead of 20 deg) or higher concentration of chemicals or all three.
It's pretty simple, really. If you're using HC-110, use concentration of 1+100 (5ml HC-110 + 500 ml water) at 27 degrees (room temperature in Singapore) for 20 minutes, agitating only first 10 secs. Very nice tones.
Tri-X is VERY VERY forgiving, and at the risk of incurring the wrath of purists, I would say you can expose anywhere between 400 and 1600 and still get very good negatives with the above method.