The next antiphon is O Clavis David. After Jesse, comes David, but this also points towards St Peter, as Jesus gave him the keys to the kingdom.
O Clavis David, et sceptrum domus Israel; qui aperis, et nemo claudit; claudis, et nemo aperit: veni, et educ vinctum de domo carceris, sedentem in tenebris, et umbra mortis.
O Key of David and sceptre of the House of Israel; you open and no one can shut; you shut and no one can open: Come and lead the prisoners from the prison house, those who dwell in darkness and the shadow of death.
Here is a nice video: