The most common and most likely answer to this crossword clue is the 12 plus 1 letter word SPIRITUALIST A
I've seen this crossword clue in The Sunday Telegraph
S
P
I
R
I
T
U
A
L
I
S
T
A
Buddy explains!
The straight part
We know that "Participant in session with board resulting in happy medium if successful?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case participant in session with board resulting in happy medium if successful? = spiritualist a.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.