The most common and most likely answer to this crossword clue is the 2 plus 3 plus 5 letter word AT ALL COSTS
I've seen this crossword clue in Financial Times
A
T
A
L
L
C
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S
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S
More clues leading to the result AT ALL COSTS
- American demanding expenses whatever happens
- A big bed’s required to hold son, no expense spared
- Class total must be sorted out, no matter what
- Come what may, a high street’s secured by companies
- Total class trained regardless of expense
- Put little son in a high bed before start of supper, whatever may happen
- Incredible payments must be made to support area, no matter what
- A large Scot's cavorting, come what may
- A lanky Scot’s running, no matter what the consequences may be
- No matter what, a dubious company will be on street corners at last
Buddy explains!

The straight part
We know that "no matter what" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case no matter what = at all costs.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.