Separation anxiety is a developmental stage, not a fault in the child or the parent. It peaks somewhere in the second year and resurfaces whenever something changes — a new school most of all. A child who cries at the gate for a week and then stops has done exactly what children do. The crying is not evidence that the decision was wrong.
Some children settle in three days and some take three weeks, and both are normal. If you are worried about your own child specifically, raise it with your paediatrician as well as with us.