The most common and most likely answer to this crossword clue is the 8 letter word INGRAINS
I've seen this crossword clue in The Times
I
N
G
R
A
I
N
S
More clues leading to the result INGRAINS
Buddy explains!

The straight part
We know that "Impresses" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case impresses = ingrains.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 INGRAINS mean?
INGRAINS verb- To dye with a fast or lasting colour.
- To make (something) deeply part of something else.