en_tn/act/09/40.md

put them all out

In this case, Peter did have everyone leave so he could be alone to pray for Tabitha.

This matter became known

The miracle of Peter raising Tabitha from the dead.

believed on the Lord

This is metonymy for "believed in the gospel of the Lord Jesus". (See: rc://en/ta/man/translate/figs-metonymy)

It happened that Peter stayed

"It came about that Peter stayed"