The most common and most likely answer to this crossword clue is the 8 letter word ETIOLATE
I've seen this crossword clue in The Daily Telegraph
E
T
I
O
L
A
T
E
More clues leading to the result ETIOLATE
Buddy explains!

The straight part
We know that "grow pale" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case grow pale = etiolate.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 ETIOLATE mean?
ETIOLATE verb- To make pale through lack of light, especially of a plant.
- To make pale and sickly-looking.
- To become pale or blanched.
- Etiolated