The most common and most likely answer to this crossword clue is the 3 plus 3 letter word NOD OFF
N
O
D
O
F
F
More clues leading to the result NOD OFF
- Consent of female to fall asleep
- Fond of bubbly, slowly lose consciousness
- Fall asleep with cap on?
- Small number remove clothing and fall asleep
- Fall asleep? Certainly not with party very loud
- 17 Sleep but refuse to remove hat (3,3
- Absolutely not getting lift, crash
- Small number may get lift or fall asleep
- Note frequencies after turning on ‘snooze’
- Contrary fellow and old females go out
Buddy explains!

The straight part
We know that "Fall asleep" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fall asleep = nod off.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.