I get the impression (and please forgive me if I am mistaken) that you have not read 1 Clement, because if you had, you would know why Clement does not mention Paul.  Clement wrote around AD 95-100, about 30 years after Paul died.  His topic had nothing whatsoever to do with Paul.  You should look the letter up on line and read it.  You will see that there was no occasion in the letter to mention the names of apostles that Clement met.  There are tens of thousands of things that Clement did not mention.  He did not mention his mother.  He did not mention who was emperor at the time.  If you read the topic that Clement addressed, there was no reason for him to mention Paul or of his personal friendship, which had ended 30 years earlier when Paul died.  We do not know a lot about Clement.  Christian tradition has him converted before Peter was killed, which is likely but not for sure.  I honestly do not know when he was converted, but we cannot be fully sure than he even met Paul or any of the apostles personally. He was made bishop of Rome in AD 88, almost 25 years after Paul died. In his letter, Clement was not discussing which apostles he knew.  He was not even talking about his own personal life.  There is no reason for him to mention the apostles.  In this letter to you, I have not mentioned my wife (until just now).  Does this mean that I am not married?  The things that Clement did not mention in his letter tell us virtually nothing.

However, Clement is clearly aware of Paul because he quotes Paul at least twice.  Specifically  1Clem 13:1 Let us therefore be lowly minded, brethren, laying aside all arrogance and conceit and folly and anger, and let us do that which is written. For the Holy Spirit says, “Let not the wise man boast in his wisdom, nor the strong in his strength, neither the rich in his riches; but he that boast, let him boast in the Lord, that he may seek Him out, and do judgment and righteousness most of all remembering the words of the Lord Jesus which He spoke, teaching forbearance and long-suffering.” This is a quote from 1 Corinthians 1:31  Also there is 1Clem 34:8 For He says, “Eye has not seen and ear has not heard, and it has not entered into the heart of man what great things He has prepared for them that patiently await Him.”  This is a quote from 1 Cor 2:9  Clearly, then, Clement was aware of Paul, as he quoted his books.Skeptics have used the fact that Clement does not mention Paul as evidence that Paul did not exist, or that his influence on the church was much less than most Christians think.  This an argument from lack of information which is a very weak argument indeed.  We should not be swayed by such arguments.  Now, if Clement were writing a history of the church in Rome and did not mention Paul, that would mean something!  But this is not the case.  As it is, the fact that he does not mention his having met the apostles in the letter 1 Clement tells us nothing.

John Oakes