The most common and most likely answer to this crossword clue is the 4 letter word SPUR
I've seen this crossword clue in The Times
S
P
U
R
More clues leading to the result SPUR
- Stimulus almost certain to overcome pressure
- Briefly turn down side road
- Turn down short side road
- Encourage sudden effort to knock out finalist?
- Goad retreating rugby players heartlessly
- Cats purr a bit with encouragement
- Gush, giving up time to offer encouragement
- Bird dropped from flower branch
- Endlessly reject encouragement
- Inspire scorn, dropping name
Buddy explains!

The straight part
We know that "Encourage" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case encourage = spur.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 SPUR mean?
SPUR noun- A rigid implement, often roughly y-shaped, that is fixed to one's heel for the purpose of prodding a horse. Often worn by, and emblematic of, the cowboy or the knight.
- A jab given with the spurs.
- Anything that inspires or motivates, as a spur does a horse.
- An appendage or spike pointing rearward, near the foot, for instance that of a rooster.
- Any protruding part connected at one end, for instance a highway that extends from another highway into a city.
- Roots, tree roots.
- A mountain that shoots from another mountain or range and extends some distance in a lateral direction, or at right angles.
- A spiked iron worn by seamen upon the bottom of the boot, to enable them to stand upon the carcass of a whale to strip off the blubber.
- A brace strengthening a post and some connected part, such as a rafter or crossbeam; a strut.
- The short wooden buttress of a post.
- A projection from the round base of a column, occupying the angle of a square plinth upon which the base rests, or bringing the bottom bed of the base to a nearly square form. It is generally carved in leafage.
- Ergotized rye or other grain.
- A wall in a fortification that crosses a part of a rampart and joins to an inner wall.
- A piece of timber fixed on the bilgeways before launching, having the upper ends bolted to the vessel's side.
- A curved piece of timber serving as a half to support the deck where a whole beam cannot be placed.
- A branch of a vein.
- A very short branch line of a railway line.
- A short thin side shoot from a branch, especially one that bears fruit or, in conifers, the shoots that bear the leaves.
- To prod (especially a horse) on the side or flank, with the intent to urge motion or haste, to gig.
- To urge or encourage to action, or to a more vigorous pursuit of an object
- To put spurs on.
- To press forward; to travel in great haste.
- A tern.
- A spurious tone, one that interferes with a signal in a circuit and is often masked underneath that signal.
- The track of an animal, such as an otter; a spoor.
- To ask, to inquire