How is the Zakat calculated on a sum of money exceeding the Nisab, which has accumulated over two and a half years due to a delayed job promotion? Is Zakat due on it immediately upon receipt, or after a full year has passed?

You are obligated to pay Zakat (definition) on the money you received for all the years since it reached the nisab (definition) (minimum threshold), because it is considered an increase in wages. And as time passed, your ownership over the equivalent of the wages became established. The delay in delivery does not necessitate Zakat until after possession, as mentioned by Imam An-Nawawi.