The most common and most likely answer to this crossword clue is the 6 letter word HAYBOX
I've seen this crossword clue in The Times
H
A
Y
B
O
X
Buddy explains!

The straight part
We know that "one can continue cooking" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one can continue cooking = haybox.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 HAYBOX mean?
HAYBOX noun- A chest insulated with a layer of hay or another insulant, formerly used to keep food hot.