The most common and most likely answer to this crossword clue is the 10 letter word DEMOCRATIC
I've seen this crossword clue in The Daily Telegraph
D
E
M
O
C
R
A
T
I
C
More clues leading to the result DEMOCRATIC
- Popular comic rated poorly
- About to include Republican in vernacular description of her opponents?
- Detectives arresting sailor come over with all having their say
- Oddly comedic art for party in US
- March — and arctic winds, showing no favours
- Comrade is disturbed with nervous reaction from American party
- Popular satire about a sailor caught turning up without hat
- … popular comic rated very high
- Popular as arctic winds after March
Buddy explains!

The straight part
We know that "with all having their say" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case with all having their say = democratic.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 DEMOCRATIC mean?
DEMOCRATIC adjective- Pertaining to democracy; favoring democracy, or constructed upon the principle of government by the people.
- Relating to a political party so called; usually, Democratic.
- Exhibiting social equality, egalitarian (see online Oxford).