1. An investigator will have to search the crime scene. - будущее.
An investigator had to search the crime scene. - прошедшее.
2. She will be able to speak English. - будущее.
She was able to speak English. - прошедшее.
3. He/she(?) will be allowed to come to the party. - будущее.
He/she(?) was allowed to come to the party. - прошедшее.