The most common and most likely answer to this crossword clue is the 8 letter word SELENIUM
I've seen this crossword clue in Independent
S
E
L
E
N
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M
More clues leading to the result SELENIUM
Buddy explains!

The straight part
We know that "element (no 34)" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case element (no 34) = selenium.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does SELENIUM mean?
SELENIUM noun- A nonmetallic chemical element (symbol Se) with an atomic number of 34, used mainly in glassmaking and pigments and as a semiconductor.
- A single atom of this element.