We have decided on a one-off inspection tomorrow, not a recurring schedule. When the library opens, we ___ the first-floor reading room.

Explication

The future time clause correctly keeps the present simple in when the library opens, while the main clause takes will for the one-off intended action. Will have inspected would claim the inspection is finished before the doors open, reversing the stated order, and the bare past form places tomorrow's visit in the past.