The most common and most likely answer to this crossword clue is the 7 letter word DEPLORE
I've seen this crossword clue in Financial Times
D
E
P
L
O
R
E
More clues leading to the result DEPLORE
- Duke to look round, dropping Times in censure
- Deeply regret daughter learning about record
- Condemn daughter and Romeo getting admission to elope at sea
- Object to banks in dire place, journey regularly taken
- Mourn eccentric old peer
- Express disapproval of traditional history written by deputy
- Mourn ailing old peer
- Disapprove of waving red pole
- Feel grief for dead and record traditions
- Record in old collection has soldiers’ lament
Buddy explains!

The straight part
We know that "Deeply regret" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case deeply regret = deplore.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 DEPLORE mean?
DEPLORE verb- To bewail; to weep bitterly over; to feel sorrow for.
- To condemn; to express strong disapproval of.
- To regard as hopeless; to give up.