The most common and most likely answer to this crossword clue is the 9 letter word STONEWALL
I've seen this crossword clue in The Daily Telegraph
S
T
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N
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L
More clues leading to the result STONEWALL
- Obstruct and delay, admitting nothing topical
- Nearly finish novel, then complete block
- Hold up progress, defending one wicket?
- Pen gripping love novel to reveal nothing
- Responds to new allegations about delay in parliament
- One with an interest in drawing may choose to do it
- Delay in overtures to new alliance
- Play for time protecting whole wicket
- Hedge surrounds united with hedge
- Doggedly obstruct rural division
Buddy explains!

The straight part
We know that "Doggedly obstruct" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case doggedly obstruct = stonewall.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 STONEWALL mean?
STONEWALL noun- A wall made from stone.
- An obstruction.
- A refusal to cooperate.
- An alcoholic drink popular in colonial America, consisting of apple cider (or sometimes applejack) mixed with rum (or sometimes gin or whisky).
- To obstruct.
- To refuse to answer or cooperate, especially in supplying information.
- Certain, definite.