Allosaurus

An allosaurus on the party's side is almost always a druid wild shape, a ranger's animal companion that has hit the dinosaur tier, or a beast tamed and transported by a circus or a frontier lord. Pick one and lean on it. The dinosaur itself has Int 2 and no languages, so any "ally" framing is really a frame for whoever is steering it.

Use the speed. A mounted allosaurus is one of the fastest land vehicles in the game at 60 ft., and it can carry a Medium rider easily given the Large size. In overland chase scenes or skirmishes against fleeing enemies, the dinosaur's job is to close gaps the party can't close on foot. In melee, it bites the thing the handler points at, and it keeps biting that thing until either the target drops or the handler signals otherwise.

The interesting tension is control. A wild shape druid runs the dinosaur cleanly, but a tamed beast wants to chase the rabbit, eat the goat, and 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 like they're holding a leash, not driving a chariot.

Don't let the dinosaur talk, plan, or feel. When the day's work is done, it lies down somewhere warm and goes to sleep, and that's the whole arc of its inner life.

An allosaurus is a chase scene that hits like a tank. The 60 ft. walk speed is the headline. Most parties move 30, the fast members move 35, and a wizard with longstrider hits 40. Nothing in a typical level 3 or 4 group outruns this thing on open ground, so the encounter design question is what terrain you put between the dinosaur and the panicking PCs.

Open with the noise. Allosaurus has Passive Perception 15, so it has already heard the party long before they see it. The first round is the chase: the dinosaur covers 60 feet, the squishiest party member is in melee range, and someone has to choose between casting and running. With 51 HP and AC 13 it folds quickly to focused fire, so the fight only lasts two or three rounds, but those rounds are brutal because of the speed differential. Position the encounter so the party can't simply scatter into trees or rocks on turn one. Make them earn the cover.

This is an Int 2 beast with no language and no tactical sense. It picks the closest thing that smells like meat and commits. If the party splits and someone breaks line of sight, the dinosaur stays on whoever is in front of it rather than chasing the runner. Use that. A clever party can buy a downed friend's life by having one PC sprint perpendicular to the chase line and yell. Reward the play.

Retreat happens when the allosaurus is bloodied and a meal is available. If a horse, a mule, or an unconscious henchman is closer than the party, it grabs that and lopes off to eat in peace. Beasts don't fight to the death over abstract grudges. They fight until they're hurt, and then they take what they can carry.

Have the players hear the footfalls a full round before they see the creature. Two heavy thuds, then one more, then the trees open.