Cryptic crossword clue
Finest cover’s a quilt made last century 3-7

The most common and most likely answer to this crossword clue is the 3 plus 7 letter word TOP QUALITY

I've seen this crossword clue in Financial Times
T
O
P
Q
U
A
L
I
T
Y

Buddy explains!

The straight part
We know that "Finest" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case finest = top quality.
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 TOP QUALITY mean?

TOP QUALITY adjective
  1. Of the highest quality; extremely good

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