The most common and most likely answer to this crossword clue is the 6 letter word STAYER
I've seen this crossword clue in The Times
S
T
A
Y
E
R
More clues leading to the result STAYER
- Tenacious horse: famous name carrying you
- You may be enthralled by celebrity who keeps going?
- I will do well in the long run to move you into the sun
- One enduring celebrity welcomes you
- One’s persistent — in a way always right
- Street philosopher one unlikely to give up
- Distinguished performer carrying you once, an enduring ride
- Celebrity hoarding a lot of currency is durable figure
- Time inside, dreadful years, he’ll survive
- Saint and philosopher who won’t give up?
Buddy explains!

The straight part
We know that "One enduring" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one enduring = stayer.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 STAYER mean?
STAYER noun- One who, or that which, upholds or supports; a prop.
- One who, or that which, stays, stops, or restrains.
- An athlete, horse, etc. with staying power.