The most common and most likely answer to this crossword clue is the 3 plus 2 letter word LIE IN
I've seen this crossword clue in The Daily Telegraph
L
I
E
I
N
More clues leading to the result LIE IN
- “They regularly retire every year at proper intervals to — of the spleen”
- Prolonged horizontality that is limited by short line
- Delay arising when not tellin’ the truth in hearing
- Pork pie — popular weekend indulgence?
- Rise late, about one will be right
- Romance at home, so stay longer beneath the sheets
- Catch up with rest of fiction
- Keep one’s head down — Eastender’s fibbing, we hear
- Make a late start with invention at home
- Invention at home providing extended enjoyment between the sheets?
Buddy explains!

The straight part
We know that "Keep one’s head down" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case keep one’s head down = lie in.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 LIE IN mean?
LIE IN noun- A period spent lying in bed for longer than usual after one has woken up.
- A form of protest where a group of people lie down in a public area.