The most common and most likely answer to this crossword clue is the 6 plus 2 plus 3 plus 7 letter word APPEAL TO THE COUNTRY
I've seen this crossword clue in The Times
A
P
P
E
A
L
T
O
T
H
E
C
O
U
N
T
R
Y
Buddy explains!
The straight part
We know that "Hold an election" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case hold an election = appeal to the country.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.