The most common and most likely answer to this crossword clue is the 4 plus 4 letter word ROCK HARD
I've seen this crossword clue in The Guardian
R
O
C
K
H
A
R
D
Buddy explains!

The straight part
We know that "utterly unyielding" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case utterly unyielding = rock hard.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 ROCK HARD mean?
ROCK HARD adjective- As tough, hard, or inflexible as a piece of rock.
- With muscles developed and toned to a high degree, especially the muscles of the abdomen.
- Having a very fully erect and stiff penis
- With strongly held beliefs and opinions, deep conviction.