The most common and most likely answer to this crossword clue is the 6 letter word RELISH
I've seen this crossword clue in The Times
R
E
L
I
S
H
Buddy explains!

The straight part
We know that "Greatly enjoy/sauce" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case greatly enjoy/sauce = relish.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 RELISH mean?
RELISH noun- A pleasant taste
- Enjoyment; pleasure.
- A quality or characteristic tinge.
- (followed by "for") A taste (for); liking (of); fondness.
- A cooked or pickled sauce, usually made with vegetables or fruits, generally used as a condiment.
- In a wooden frame, the projection or shoulder at the side of, or around, a tenon, on a tenoned piece.
- Something that is greatly liked or savoured.
- To taste or eat with pleasure, to like the flavor of
- To take great pleasure in.
- To taste; to have a specified taste or flavour.
- To give a taste to; to cause to taste nice, to make appetizing.
- To give pleasure.