The most common and most likely answer to this crossword clue is the 6 letter word HELPED
I've seen this crossword clue in The Guardian
H
E
L
P
E
D
More clues leading to the result HELPED
Buddy explains!

The straight part
We know that "promoted" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case promoted = helped.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 HELPED mean?
HELPED verb- To provide assistance to (someone or something).
- To assist (a person) in getting something, especially food or drink at table; used with to.
- To contribute in some way to.
- To provide assistance.
- To avoid; to prevent; to refrain from; to restrain (oneself). Usually used in nonassertive contexts with can.