Allosaurus

An allosaurus on the party's side is almost always a druid wild shape, a ranger's beast that has grown into the dinosaur tier, or a creature tamed and transported by a traveling circus or a frontier lord. The dinosaur has Int 2 and no languages, so the real "ally" is whoever is steering it. Play that control as the tension.

Use the speed. A mounted allosaurus is one of the fastest land vehicles in the game at 60 ft., and it carries a Medium rider easily at Large size. In overland chases or skirmishes against fleeing enemies, it closes gaps the party cannot. In melee, it attacks whatever the handler points at and keeps attacking that target until it drops or the handler signals shift.

A wild shape druid runs the dinosaur cleanly. A tamed beast wants to chase the rabbit, eat the goat, ignore the cobbler the party was trying to protect. Roll a Wisdom (Animal Handling) check at the start of any scene where the dinosaur has multiple available targets. On a fail, it picks the wrong one. The party should feel they are holding a leash, not driving a chariot.

When the day ends, the dinosaur lies down somewhere warm and sleeps. That is the whole arc of its inner life.

An allosaurus is a chase predator, not a stand-and-fight tank. The 60 ft. walk speed is what you're selling, and it runs the encounter from pure mobility. Most parties move 30 to 35 feet per turn; a wizard with longstrider hits 40. On open ground, nothing catches this dinosaur if it doesn't want to be caught, and nothing escapes it if it does.

Use the first round for the hunt, not the fight. The allosaurus has Passive Perception 15, so it smells the party long before they see it. Position the encounter so the party can't scatter into rocks or forest on turn one. When combat starts, the dinosaur closes 60 feet, puts the squishiest member in melee range, and now someone has to choose between casting and running. The Claws attack knocks a Large or smaller creature Prone if the allosaurus has moved at least 30 feet straight toward it, which it absolutely will have on turn one. A Prone target takes the Bite on top of the Claws. That's 8 plus 15 damage in one burst, and most low-level squishies don't survive the combo.

This is an Int 2 beast with no sense of strategy. It picks the closest meal and commits to it. If the party splits and someone breaks line of sight, the dinosaur stays on whoever is in front of it. Use that fact. A clever party can buy a downed friend's life by having one PC sprint perpendicular to the chase and yell. The dinosaur won't chase the noise over what it can see and smell.

Once the allosaurus is bloodied and there's an escape route, it takes it. Grab a horse, a mule, an unconscious henchman if one is closer than the party. Beasts don't die fighting for pride. They fight until they hurt, then they eat in peace. Have the players hear the footfalls a full round before they see it. Two heavy thuds, then one more, then the trees open.