The most common and most likely answer to this crossword clue is the 9 letter word STREAMLET
I've seen this crossword clue in The Guardian
S
T
R
E
A
M
L
E
T
More clues leading to the result STREAMLET
Buddy explains!

The straight part
We know that "A little current" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a little current = streamlet.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 STREAMLET mean?
STREAMLET noun- A small stream.