The most common and most likely answer to this crossword clue is the 8 plus 7 letter word RELATIVE PRONOUN
I've seen this crossword clue in The Times
R
E
L
A
T
I
V
E
P
R
O
N
O
U
N
More clues leading to the result RELATIVE PRONOUN
- No value in report scrapped, which could be this
- Who, say, is lover involved with piano tuner?
- Maybe that family member supporting sister with nothing to hide
- What that might be?
- Maybe what could make inventor pour ale
- Say which arrangement of Beethoven’s last piano overture includes cello in the middle
Buddy explains!

The straight part
We know that "What that might be?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case what that might be? = relative pronoun.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.