The most common and most likely answer to this crossword clue is the 4 letter word KEEP
K
E
E
P
Buddy explains!

The straight part
We know that "Observe/delay" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case observe/delay = keep.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 KEEP mean?
KEEP noun- The main tower of a castle or fortress, located within the castle walls.
- The food or money required to keep someone alive and healthy; one's support, maintenance.
- The act or office of keeping; custody; guard; care; heed; charge; notice.
- The state of being kept; hence, the resulting condition; case.
- That which is kept in charge; a charge.
- A cap for holding something, such as a journal box, in place.
- To continue in (a course or mode of action); not to intermit or fall from; to uphold or maintain.
- (heading) To hold the status of something.
- (heading) To hold or be held in a state.
- To wait for, keep watch for.
- To act as wicket-keeper.
- To take care; to be solicitous; to watch.
- To be in session; to take place.
- To observe; to adhere to; to fulfill; not to swerve from or violate.
- (by extension) To visit (a place) often; to frequent.
- To observe or celebrate (a holiday).