The most common and most likely answer to this crossword clue is the 5 plus 3 plus 5 letter word TURNS THE SCREW
I've seen this crossword clue in The Daily Telegraph
T
U
R
N
S
T
H
E
S
C
R
E
W
Buddy explains!
The straight part
We know that "Puts pressure on" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case puts pressure on = turns the screw.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.