The most common and most likely answer to this crossword clue is the 13 plus 5 letter word PHILOSOPHER'S STONE
I've seen this crossword clue in The Times
P
H
I
L
O
S
O
P
H
E
R
'
S
S
T
O
N
E
Buddy explains!
The straight part
We know that "It's what many have sought" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case it's what many have sought = philosopher's stone.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.