Elapsed from?
This is what happens when you try to write 'smart' and fail.
Domitian narrowly escaped being killed in the fighting in Rome in December 69 between Vitellius' supporters and his father's supporters (Vespasian was not yet in Rome). A lot of Romans later wished he had been killed then.
The word “that” refers to the period of time from the death of Domitian to the accession of Commodus. “The period which elapsed...” is perfectly good grammar.