The most common and most likely answer to this crossword clue is the 5 plus 5 letter word DRIFT APART
I've seen this crossword clue in The Guardian
D
R
I
F
T
A
P
A
R
T
More clues leading to the result DRIFT APART
Buddy explains!
The straight part
We know that "gradually become estranged" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case gradually become estranged = drift apart.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.