The most common and most likely answer to this crossword clue is the 9 letter word TARDINESS
I've seen this crossword clue in The Daily Telegraph
T
A
R
D
I
N
E
S
S
More clues leading to the result TARDINESS
- Delay lunches consumed by sailors
- Inserts ad after confusing delay
- Being behind, rise, stand another way
- Lateness of sailors holding banquets
- Is stander around demonstrating this?
- Takes a meal among sailors, though it causes delay
- Senior going back in time machine, arriving late
- Unpunctuality of sailors holding banquets
- It’s snared wild sloth
- Disaster coming around about noon, being late
Buddy explains!

The straight part
We know that "Quality of slow service" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case quality of slow service = tardiness.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 TARDINESS mean?
TARDINESS noun- The state or quality of being tardy.
- The result or product of being tardy.