In the reaction \( \text{AlCl}_{3} + \text{Cl}^{-} \rightarrow \text{AlCl}_{4}^{-} \), the Al atom in \( \text{AlCl}_{3} \) initially has an sp2 hybridisation as it is bonded to three chloride ions. When a chloride ion \( \text{Cl}^{-} \) is added, the Al atom undergoes hybridisation change from sp2 to sp3 as it now forms four bonds, resulting in the formation of the tetrahedral complex \( \text{AlCl}_{4}^{-} \).