The most common and most likely answer to this crossword clue is the 11 letter word TRANSFUSION
I've seen this crossword clue in The Daily Telegraph
T
R
A
N
S
F
U
S
I
O
N
Buddy explains!
The straight part
We know that "Vital exchange in a theatre" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case vital exchange in a theatre = transfusion.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.
Crossword Answer definitions
TRANSFUSION noun- The transfer of blood or blood products from one individual to another.
- The act of pouring liquid from one vessel to another.