The most common and most likely answer to this crossword clue is the 6 letter word NESTOR
N
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S
T
O
R
More clues leading to the result NESTOR
- Regularly sneers at poor old counsellor
- Wise counsellor somehow errs on no test, ignoring duplicates
- Fine story featuring Greek
- Old and wise, he contributes to finest oratory
- ‘Not rocket science, Einstein’s principles,’ gathered wise old man
- Wise man trapped by dishonest organisation
- Wise man features in fine story
- Sage's direction gets store's rearmost section shifted
- Wise man in comfy position getting nothing right
Buddy explains!

The straight part
We know that "wise old man" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case wise old man = nestor.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.