He was found in the first episode (T-Rex Returns) amongst his sister, Matilda. Their mother is killed by another T-Rex and Nigel brings them to the Park.
Terence appears in all the episodes, and in the fifth one (The Bug House), he is bitten by Matilda. Nigel then comes in with a jeep to distract Matilda away from wounded Terence. A tranquilizer dart is fired at Matilda and while chasing Nigel it takes effect. Terence is rushed to medical care. After a very close encounter with Matilda he makes a full recovery. However, now there must be a larger fence to keep the two Tyrannosaurus Rexs away from eachother.