The most common and most likely answer to this crossword clue is the 6 plus 7 letter word PUBLIC COMPANY
P
U
B
L
I
C
C
O
M
P
A
N
Y
Buddy explains!
The straight part
We know that "corporation trading shares freely on stock exchange" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case corporation trading shares freely on stock exchange = public company.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.