The most common and most likely answer to this crossword clue is the 4 plus 4 letter word NEXT BEST
I've seen this crossword clue in The Daily Telegraph
N
E
X
T
B
E
S
T
More clues leading to the result NEXT BEST
Buddy explains!

The straight part
We know that "Thing that’s almost as good" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case thing that’s almost as good = next best.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.