The most common and most likely answer to this crossword clue is the 3 letter word WEE
I've seen this crossword clue in Financial Times
W
E
E
Buddy explains!

The straight part
We know that "A little" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a little = wee.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 WEE mean?
WEE noun- A short time or short distance.
- Small, little.
- Urine.
- An act of urination.
- To urinate.
- (personal) The speakers/writers, or the speaker/writer and at least one other person (not the person being addressed). (This is the exclusive we.)
- (personal) The speaker(s)/writer(s) and the person(s) being addressed. (This is the inclusive we.)
- (personal) The speaker/writer alone. (This use of we is the editorial we, used by writers and others, including royalty—the royal we—as a less personal substitute for I. The reflexive case of this sense of we is ourself.)
- (personal) The plural form of you, including everyone being addressed.
- (personal, often considered patronising) A second- or third-person pronoun for a person in the speaker's care.