The most common and most likely answer to this crossword clue is the 11 letter word GRASSHOPPER
I've seen this crossword clue in The Daily Telegraph
G
R
A
S
S
H
O
P
P
E
R
More clues leading to the result GRASSHOPPER
- Talk about right one looking to buy jumper
- Jumper displayed in foie gras shop, perhaps
- Chirpy sort being fat French consumer
- Six-footer seen in peach jumper
- He gives away funnel for a cocktail
- Briefly follow one looking to purchase a jumper?
- Insect found in store among squashed grapes — run!
- Hang back, keeping right next to person buying a jumper
- Talk about right before consumer finds jumper
- Sharp pegs or otherwise for small jumper
Buddy explains!

The straight part
We know that "a little green jumper" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a little green jumper = grasshopper.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 GRASSHOPPER mean?
GRASSHOPPER noun- A mostly herbivorous insect of the order Orthoptera, noted for its ability to jump long distances and for the habit of some species communicating by stridulation; they are related to but distinct from crickets.
- A cocktail made with crème de menthe and optionally with crème de cacao.
- A young student in initial stages of training who has been chosen on account of their obvious talent.
- In ordinary square or upright pianos of London make, the escapement lever or jack, so made that it can be taken out and replaced with the key.