The most common and most likely answer to this crossword clue is the 6 letter word ELDEST
I've seen this crossword clue in Financial Times
E
L
D
E
S
T
More clues leading to the result ELDEST
- First-born, European duke, taken inside just in case
- Most senior of the French embraced by English lieutenant
- In Sheffield estate, has been around the longest
- First of children to turn 13
- Part of rebel destined to be greatest in age
- First in line? Last in line? First in line? In short, the end of the line
- This son held estate implicitly
- First-born of Israel destined for central role?
- Cruel destiny imprisoning the first-born
- Real adversity oddly bypassed first-born
Buddy explains!

The straight part
We know that "has been around the longest" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case has been around the longest = eldest.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 ELDEST mean?
ELDEST noun- The eldest child in a family, or individual in a group.
- (of a player) Receiving cards from the dealer first, before any other players.
- (of a hand) Having higher, or superior cards.
- Of an object, concept, relationship, etc., having existed for a relatively long period of time.
- Having been used and thus no longer new or unused.
- Having existed or lived for the specified time.
- (heading) Of an earlier time.
- Tiresome after prolonged repetition.
- Said of subdued colors, particularly reds, pinks and oranges, as if they had faded over time.
- A grammatical intensifier, often used in describing something positive. (Mostly in idioms like good old, big old and little old, any old and some old.)
- Excessive, abundant.