The most common and most likely answer to this crossword clue is the 9 letter word DEEPENING
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Buddy explains!

The straight part
We know that "Increasing depth" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case increasing depth = deepening.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 DEEPENING mean?
DEEPENING verb- To make deep or deeper
- To make darker or more intense; to darken
- To make more poignant or affecting; to increase in degree
- To make lower in tone
- To make more thorough or extensive.
- To make more intimate.
- To make more sound or heavy.
- To become deeper
- To become darker or more intense
- To become lower in tone
- To become more thorough or extensive.
- To become more intimate.
- To become more sound or heavy.
- The act of becoming deeper.