The most common and most likely answer to this crossword clue is the 16 letter word PRESSÂ CONFERENCE
I've seen this crossword clue in The Guardian
P
R
E
S
S
Â
C
O
N
F
E
R
E
N
C
E
Buddy explains!
The straight part
We know that "At which to keep questioning Labour gathering" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case at which to keep questioning labour gathering = press conference.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.