Tolkien once wrote that Legolas recognized Imrahil as part elven because no elves or part elves have beards.
So why did he write that Círdan had a beard?
Most of the ordinary elves mentioned in LOTR might be only 457, or 1,519, or 2,821, years old when mentioned.
Círdan was described in year 3021 of the Third Age. The Second Age lasted for 3441 years. The First Age ended 6,472 years before Círdan was described as having a beard in TA 3021. Elrond was born 58 years before the end of the First Age, and so was 6,530 years old in TA 3021.
Tolkien wrote annals giving Galadriel's birth date in Years of the Trees, but unfortunately couldn't make up his mind if the Years of the Trees in Valinor were nine point something times as long as Years of the Sun, or ten times as long, or 144 times as long as Years of the Sun.
So Galadriel is millennia older than Elrond, but depending on the length of Years of the Trees, she could be 14.4 times as many millennia older.
And nobody knows the relative ages of Círdan and Celeborn. Círdan was an important leader of elves far back in the Elder Days, ere ever Galadrial's father was born.
Celeborn is probably a youngster compared to Círdan, no older than Galadrial, but might possibly be as old or older than Círdan. Tolkien kept changing the backstory of Galadrial and Celeborn (including Celeborn's genealogy) trying to get it right, so nobody knows.
So Círdan in the year Third Age 3021 is probably the oldest elf described in Tolkien's works, probably by thousands of years and possibly by tens of thousands.
Tolkien once wrote a note saying that Elves didn't go beards until their third cycle of life - he didn't define cycles but elves would probably be at least ten thousand years old in their third cycle of life.
And so some Tolkien scholars believe that Círdan was the only male elf described when he was old enough to grow a beard.