The most common and most likely answer to this crossword clue is the 4 plus 6 letter word DEEP THROAT
I've seen this crossword clue in The Guardian
D
E
E
P
T
H
R
O
A
T
Buddy explains!
The straight part
We know that "River grass encircling path, not a river /grass/ (4,6)" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case river grass encircling path, not a river /grass/ (4,6) = deep throat.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.