The most common and most likely answer to this crossword clue is the 13 plus 2 letter word MIDDLESBROUGH FC
I've seen this crossword clue in Financial Times
M
I
D
D
L
E
S
B
R
O
U
G
H
F
C
Buddy explains!
The straight part
We know that "Riverside club" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case riverside club = middlesbrough fc.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.