Step 1: Approach by clinical consequence: A1AT deficiency causes emphysema, so the enzyme it normally curbs must damage lung tissue.
Step 2: That lung-damaging enzyme is neutrophil elastase, which chews up elastin in alveolar walls.
Step 3: A1AT, a liver-made serpin, binds and neutralises elastase, keeping the protease-antiprotease balance in favour of intact connective tissue.
Step 4: When A1AT is low, elastase runs free and panacinar emphysema follows. The mechanism asked is inhibition of elastase, not trypsin, trypsinogen or chymotrypsin.
\[\boxed{\text{Inhibition of elastase}}\]