The most common and most likely answer to this crossword clue is the 9 letter word SIDELINES
I've seen this crossword clue in Financial Times
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More clues leading to the result SIDELINES
Buddy explains!

The straight part
We know that "subsidiary interests" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case subsidiary interests = sidelines.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 SIDELINES mean?
SIDELINES noun- A line at the side of something.
- Something that is additional or extra or that exists around the edges or margins of a main item.
- A line for hobbling an animal by connecting the fore and the hind feet of the same side.
- A line defining the side boundary of a playing field.
- Usually in the plural: the area outside the playing field beyond each sideline.
- The outside or perimeter of any activity.
- A secondary road, especially a byroad at right angles to a main road.
- To place on the sidelines; to bench or to keep someone out of play.
- To remove or keep out of circulation or out of the focus.