The most common and most likely answer to this crossword clue is the 8 letter word ALACRITY
I've seen this crossword clue in The Guardian
A
L
A
C
R
I
T
Y
More clues leading to the result ALACRITY
- Keenness from Republican entering in urban style?
- Expedition to the French metropolis must cross river
- Dispatch a group of ordinary people across Costa Rica
- Eagerness of first-rate amateurs to take credit
- Speed of a non-professional penning short review
- Haste required, needing endless walk right through a city
- Clay Rita modelled, showing eager promptness
- Eagerness in the manner of big town needing to entertain queen
- Expedition to the French metropolis goes round river
- Smartness? To the French, Paris say, holds recipe
Buddy explains!

The straight part
We know that "Dispatch" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dispatch = alacrity.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 ALACRITY mean?
ALACRITY noun- Eagerness; liveliness; enthusiasm.
- Promptness; speed.