The most common and most likely answer to this crossword clue is the 6 letter word DOTING
I've seen this crossword clue in Financial Times
D
O
T
I
N
G
More clues leading to the result DOTING
Buddy explains!

The straight part
We know that "Loving" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case loving = doting.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 DOTING mean?
DOTING verb- (usually with on) To be weakly or foolishly fond of somebody.
- To act in a foolish manner; to be senile.
- Excessive fondness; reverence.
- Characterized by giving love and affection.