The most common and most likely answer to this crossword clue is the 7 plus 2 plus 6 letter word EXPENSE NO OBJECT
I've seen this crossword clue in Financial Times
E
X
P
E
N
S
E
N
O
O
B
J
E
C
T
Buddy explains!
The straight part
We know that "regardless of cost" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case regardless of cost = expense no object.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.