The most common and most likely answer to this crossword clue is the 4 letter word WHET
I've seen this crossword clue in Independent
W
H
E
T
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 = whet.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 WHET mean?
WHET noun- The act of whetting something.
- That which whets or sharpens; especially, an appetizer.
- To hone or rub on with some substance, as a piece of stone, for the purpose of sharpening – see whetstone.
- To stimulate or make more keen.
- To preen.