The most common and most likely answer to this crossword clue is the 7 letter word FEATHER
I've seen this crossword clue in The Guardian
F
E
A
T
H
E
R
More clues leading to the result FEATHER
- Old man holding end of mauve quill
- Old man grabbing eastern bird's plume
- Apprehension about the quill
- Boxer’s achievement — and the woman’s importance
- Just one of the things that get you down?
- Large lady’s eating last of cake, a little down
- Afraid to grip the wedge?
- Dread holding the light thing
- Priest swallows drug — it helps in flight
- Lightly touch on that woman’s achievement first
Buddy explains!

The straight part
We know that "wedge" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case wedge = feather.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 FEATHER mean?
FEATHER noun- A branching, hair-like structure that grows on the bodies of birds, used for flight, swimming, protection and display.
- Long hair on the lower legs of a dog or horse, especially a draft horse, notably the Clydesdale breed. Narrowly only the rear hair.
- One of the fins or wings on the shaft of an arrow.
- A longitudinal strip projecting from an object to strengthen it, or to enter a channel in another object and thereby prevent displacement sideways but permit motion lengthwise; a spline.
- Kind; nature; species (from the proverbial phrase "birds of a feather").
- One of the two shims of the three-piece stone-splitting tool known as plug and feather or plug and feathers; the feathers are placed in a borehole and then a wedge is driven between them, causing the stone to split.
- The angular adjustment of an oar or paddle-wheel float, with reference to a horizontal axis, as it leaves or enters the water.
- Anything petty or trifling; a whit or jot.
- (in the plural) Partridges and pheasants, as opposed to rabbits and hares (called fur).
- To cover or furnish with feathers.
- To arrange in the manner or appearance of feathers.
- To rotate the oars while they are out of the water to reduce wind resistance.
- To streamline the blades of an aircraft's propeller by rotating them perpendicular to the axis of the propeller when the engine is shut down so that the propeller does not windmill during flight.
- To finely shave or bevel an edge.
- To intergrade or blend the pixels of an image with those of a background or neighboring image.
- To adorn, as with feathers; to fringe.
- To render light as a feather; to give wings to.
- To enrich; to exalt; to benefit.
- To tread, as a cock.
- To accidentally touch the cue ball with the tip of the cue when taking aim