The most common and most likely answer to this crossword clue is the 7 letter word DESERTS
I've seen this crossword clue in The Times
D
E
S
E
R
T
S
More clues leading to the result DESERTS
- Just rewards — puddings. by the sound of it
- Leaves sweets for the Speaker
- Abandons son leaving courses
- Rats in areas of wasteland
- See 1 across
- Leaves sweets for the audience
- Leaves behind places of solitude
- Places with little vegetation or leaves
- Wastes rewards
- Primarily desolate and covered in sand – trees rarely found in these
Buddy explains!

The straight part
We know that "Just rewards" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case just rewards = deserts.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 DESERTS mean?
DESERTS noun- (usually in the plural) That which is deserved or merited; a just punishment or reward
- A barren area of land or desolate terrain, especially one with little water or vegetation; a wasteland.
- Any barren place or situation.
- To leave (anything that depends on one's presence to survive, exist, or succeed), especially when contrary to a promise or obligation; to abandon; to forsake.
- To leave one's duty or post, especially to leave a military or naval unit without permission.