The Te Mata Peak Park has a small network of about 15km of singletrack - all of it on the side the famous hill to the east of Hastings. There are good map boards at the main access points to the trails showing the trail grades, names and routes.
It's not a network for beginners - the best trails need at least intermediate skills and they tend to be steep.
Typically people start at the Tauroa Road car park, ride up Chambers walkway, then use the climbing singletrack (it's good!) that starts near the Main Gates Car Park and goes up beside the road. At the top of it you'll find a well designed flowing trail that starts by Te Mata Peak Road and heads on down the hill with lots of rollers, a few drops, a nice chute, and plenty of opportunities for air if you can handle a narrow landing track.
By the way, there are great views from the top of Te Mata Peak and the cafes in Havelock North at the bottom of the area are celebrated.