The most common and most likely answer to this crossword clue is the 9 letter word ELONGATES
I've seen this crossword clue in The Guardian
E
L
O
N
G
A
T
E
S
Buddy explains!
The straight part
We know that "lengthens the process" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lengthens the process = elongates.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 ELONGATES mean?
ELONGATES verb- To make long or longer by pulling and stretching; to make elongated.
- To become long or longer by being pulled or stretched; to become elongated.
- To move to or place at a distance (from something).
- To depart to, or be at, a distance (from something); especially, to recede apparently from the sun, as a planet in its orbit.