Clement of Rome in the Roman list
Irenaeus places Clement third after the apostles and associates his time with Rome's letter to Corinth. The letter itself speaks in the name of the Roman church and gives no personal signature from Clement.
Primary sources
Irenaeus continues:
Irenaeus's Roman sequence places Clement third from the apostles after Linus and Anacletus.
The blessed apostles, then, having founded and built up the Church, committed into the hands of Linus the office of the episcopate. Of this Linus, Paul makes mention in the Epistles to Timothy. To him succeeded Anacletus; and after him, in the third place from the apostles, Clement was allotted the bishopric.
Passage context and translation
Irenaeus gives the Roman sequence inside an argument against secret Gnostic teaching. His passage identifies succession of office but does not name a consecrator at every link.
Before the excerpt
the faith preached to men, which comes down to our time by means of the successions of the bishops
After the excerpt
This man, as he had seen the blessed apostles, and had been conversant with them