The most common and most likely answer to this crossword clue is the 9 letter word TRIBUTARY
I've seen this crossword clue in The Daily Telegraph
T
R
I
B
U
T
A
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More clues leading to the result TRIBUTARY
Buddy explains!

The straight part
We know that "Subsidiary course" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case subsidiary course = tributary.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 TRIBUTARY mean?
TRIBUTARY noun- A natural water stream that flows into a larger river or other body of water.
- A nation, state, or other entity that pays tribute.
- Related to the paying of tribute.
- Subordinate; inferior
- Yielding supplies of any kind; serving to form or make up, a greater object of the same kind, as a part, branch, etc.; contributing.