The most common and most likely answer to this crossword clue is the 6 letter word TOP-UP
I've seen this crossword clue in The Times
T
O
P
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U
P
More clues leading to the result TOP-UP
Buddy explains!

The straight part
We know that "A little more" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a little more = top-up.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 TOP-UP mean?
TOP-UP noun- An addition.
- An additional premium paid over the initial premium in order to increase benefit values.
- Additional credit purchased for a mobile phone.
- A dose of epidural anesthetic added to previously injected spinal anesthetic in combined spinal-epidural anesthesia
- The situation where a student who holds a qualification equivalent to part of a degree course is then accepted onto a degree course at an intermediate point, without having to start it from the beginning.
- That serves as an addition