Cryptic crossword clue
Cooking fish in prison — one with new governor at its head 4-6

The most common and most likely answer to this crossword clue is the 11 letter word STIR-FRYING

I've seen this crossword clue in The Guardian
S
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F
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G

Buddy explains!

The straight part
We know that "Cooking" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cooking = stir-frying.
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 STIR-FRYING mean?

STIR-FRYING verb
  1. To fry quickly in hot oil whilst constantly stirring, especially in a wok or similar pan.

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