The most common and most likely answer to this crossword clue is the 6 plus 5 letter word ROWING COACH
I've seen this crossword clue in The Daily Telegraph
R
O
W
I
N
G
C
O
A
C
H
Buddy explains!
The straight part
We know that "One over the eight on the river" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one over the eight on the river = rowing coach.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.