The most common and most likely answer to this crossword clue is the 4 letter word SAGS
I've seen this crossword clue in Independent
S
A
G
S
Buddy explains!

The straight part
We know that "sinks" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case sinks = sags.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 SAGS mean?
SAGS noun- The state of sinking or bending; a droop.
- The difference in elevation of a wire, cable, chain or rope suspended between two consecutive points.
- The difference in height or depth between the vertex and the rim of a curved surface, specifically used for optical elements such as a mirror or lens.