The most common and most likely answer to this crossword clue is the 8 letter word CURTSEYS
I've seen this crossword clue in The Guardian
C
U
R
T
S
E
Y
S
More clues leading to the result CURTSEYS
Buddy explains!

The straight part
We know that "Gestures of respect" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case gestures of respect = curtseys.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 CURTSEYS mean?
CURTSEYS noun- A small bow, generally performed by a woman or a girl, where she crosses one calf of her leg behind the other and briefly bends her knees and lowers her body in deference.
- To make a curtsey.