The most common and most likely answer to this crossword clue is the 8 letter word FURTHERS
I've seen this crossword clue in The Daily Telegraph
F
U
R
T
H
E
R
S
Buddy explains!
The straight part
We know that "Promotes" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case promotes = furthers.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 FURTHERS mean?
FURTHERS verb- To help forward; to assist.
- To encourage growth; to support progress or growth of something; to promote.