The most common and most likely answer to this crossword clue is the 11 letter word CENTENARIAN
I've seen this crossword clue in The Daily Telegraph
C
E
N
T
E
N
A
R
I
A
N
Buddy explains!

The straight part
We know that "oldste" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case oldste = centenarian.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 CENTENARIAN mean?
CENTENARIAN noun- One who is at least 100 years old. One who is past their tenth decade.
- Being at least 100 years old. Beyond one's tenth decade.
- Of or relating to a centenarian.