The most common and most likely answer to this crossword clue is the 9 letter word HEADWATER
I've seen this crossword clue in Independent
H
E
A
D
W
A
T
E
R
Buddy explains!

The straight part
We know that "Part of stream" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case part of stream = headwater.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 HEADWATER mean?
HEADWATER noun- (chiefly in the plural) The source (and the initial part) of a stream