The most common and most likely answer to this crossword clue is the 6 letter word CAJOLE
I've seen this crossword clue in The Times
C
A
J
O
L
E
More clues leading to the result CAJOLE
- Encourage a judge to tuck into cabbage
- Persuade knave to return, mostly getting encouragement from Spanish?
- Try to persuade old king to protect a judge
- Sweet-talk head of casting over a part — Juliet, not Romeo
- Coax old king to imprison Juliet after beginning of affair
- Persuade little woman to split cold beer
- Coax ‘Heroin’ number out of John Cale on tour
- Sweet-talk king from a nursery rhyme, acquiring a piece of jewelry
- Persuade merry old king to receive heads of Al Jazeera
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 = cajole.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 CAJOLE mean?
CAJOLE verb- To persuade someone to do something which they are reluctant to do, especially by flattery or promises; to coax.