The most common and most likely answer to this crossword clue is the 7 letter word LEERING
I've seen this crossword clue in Financial Times
L
E
E
R
I
N
G
More clues leading to the result LEERING
- Eyeing up Heather, who’s always in
- Member tours old Ireland with lecherous look
- Clique hiding behind shelter lusting after woman?
- Liberal European circle supports end of inane ogling
- Reeling, a little drunk giving the glad eye
- Band behind shelter staring lasciviously
- Visibly lecherous on Emerald Isle breaks
- Pole abandoned drunk girl seen looking with lust
- Ogling the French sweetheart with girdle
- Shelter band, acting like a wolf
Buddy explains!

The straight part
We know that "Eyeing up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case eyeing up = leering.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 LEERING mean?
LEERING verb- To look sideways or obliquely; now especially with sexual desire or malicious intent.
- To entice with a leer or leers.
- To teach.
- To learn.
- Action of the verb to leer.