The most common and most likely answer to this crossword clue is the 6 letter word DEMOTE
I've seen this crossword clue in Independent
D
E
M
O
T
E
More clues leading to the result DEMOTE
- Downgrade daughter and show real feeling
- Humble cashier
- Put down sample tape, having erased contents
- Protest over central features of latest downgrade
- Act in a degrading way
- Relegate upwardly mobile young lad clutching book
- Replacing leader with daughter, far lower in rank
- Downgrade in English test welcomed by both sides in dispute
- Lower River Test cutting
Buddy explains!

The straight part
We know that "Lower" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lower = demote.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 DEMOTE mean?
DEMOTE verb- To lower the rank or status of.
- To relegate.