The most common and most likely answer to this crossword clue is the 8 letter word INDEBTED
I've seen this crossword clue in The Daily Telegraph
I
N
D
E
B
T
E
D
More clues leading to the result INDEBTED
- Owing recognition absolutely, but empty inside
- Marry holding empty bouquet being thankful
- Under an obligation, actually accepting telephone company
- Grateful Iron Duke with bravest ended losing heart
- Actually taking on phone company owing money
- Owing gratitude? Yes, but heartless inside
- Obliged really to confine basket case
- Thankful truly to accommodate bishop and knight finally
Buddy explains!

The straight part
We know that "Under an obligation" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case under an obligation = indebted.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 INDEBTED mean?
INDEBTED verb- To bring into debt; to place under obligation.
- (usually with to) Obligated, especially financially.