The most common and most likely answer to this crossword clue is the 5 plus 2 letter word TALLY HO
I've seen this crossword clue in The Times
T
A
L
L
Y
H
O
More clues leading to the result TALLY HO
Buddy explains!

The straight part
We know that "rider's remark" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case rider's remark = tally ho.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 TALLY HO mean?
TALLY HO noun- An instance of the interjection.
- A pleasure coach.
- To articulate the interjection.
- Used to urge on a fox hunt, especially when the fox is sighted.
- A simple greeting, exclusively used by the upper classes.
- Target sighted.