The most common and most likely answer to this crossword clue is the 11 letter word RETARDATION
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Buddy explains!

The straight part
We know that "Delay" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case delay = retardation.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 RETARDATION mean?
RETARDATION noun- The act of retarding or delaying; hindrance.
- The extent to which anything is retarded; the result of any retarding or delay; mental, social, or physical slowness.
- Extreme stupidity.
- That which retards; an obstacle; an obstruction.
- Deceleration; reduction in the magnitude of velocity.
- A suspension which resolves upwards.