The most common and most likely answer to this crossword clue is the 7 letter word LECTERN
I've seen this crossword clue in Independent
L
E
C
T
E
R
N
More clues leading to the result LECTERN
- Stand in church, left centre, roughly
- In church, stand erect, teetering between rear of chancel and front of nave
- Reported theatre act, having first left City desk?
- Reading desk, large, with damaged centre
- Large centre unexpectedly supplies reading desk
- Grotesque character given name has support when speaking?
- Chosen to strip off, servicemen stand before the faithful
- New centre after large reading desk
- Stand made by Hannibal close to Mediterranean?
- You are reportedly leaving academic with new Reader’s support
Buddy explains!

The straight part
We know that "support when speaking" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case support when speaking = lectern.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.
What does LECTERN mean?
LECTERN noun- A stand with a slanted top used to support a bible from which passages are read during a church service.
- A similar stand to support a lecturer's notes.