The most common and most likely answer to this crossword clue is the 8 letter word NUTRIENT
I've seen this crossword clue in The Times
N
U
T
R
I
E
N
T
More clues leading to the result NUTRIENT
- Sustenance teachers finally sought, eating nothing in Paris
- Character by river absorbing current source of nourishment
- Zealot on charter round island promoting growth
- Seed payment I invested, promoting growth
- Food fanatic: “Nothing in Paris arrives on time”
- Lunatic tore round island for sustenance
- Brazil may be nothing to France, having the ultimate in restaurant food
- Nourishment can be obtained from a ginger biscuit — tip off football team
- Something good to eat in inn? True, after revamp. Tons!
- Tucking into bananas endlessly, there’s nothing for Frenchman to make healthy bit of food
Buddy explains!

The straight part
We know that "promoting growth" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case promoting growth = nutrient.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 NUTRIENT mean?
NUTRIENT noun- A source of nourishment, such as food, that can be metabolized by an organism to give energy and build tissue.
- Providing nourishment.