The most common and most likely answer to this crossword clue is the 4 letter word LEER
I've seen this crossword clue in The Guardian
L
E
E
R
More clues leading to the result LEER
- Stagger back and stare
- Lecherous look from king when speaking
- Notice omitted from editorial? That's an odd look
- Stagger back, giving lecherous look
- Lecherous look making us stagger backwards
- Recipe requiring fish to be turned over in oven
- Unpleasant look of heartless landlord
- Lecherous look makes you stagger back
- Drugs grasped by both hands eliciting a sideways look
- Stagger backwards giving lecherous gaze
Buddy explains!

The straight part
We know that "suggestive look" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case suggestive look = leer.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 LEER mean?
LEER noun- A significant side glance; a glance expressive of some passion, as malignity, amorousness, etc.; a sly or lecherous look.
- An arch or affected glance or cast of countenance.
- To look sideways or obliquely; now especially with sexual desire or malicious intent.
- To entice with a leer or leers.
- The cheek.
- The face.
- One's appearance; countenance.
- Complexion; hue; colour.
- Flesh; skin.
- The flank or loin.
- Empty; unoccupied; clear.
- Destitute; lacking; wanting.
- Faint from lack of food; hungry.
- Thin; faint.
- Having no load or burden; free; without a rider.
- Lacking sense or seriousness; trifling; frivolous.
- To teach.
- To learn.
- A long oven or kiln, often having a moving belt, used for annealing glass.