The most common and most likely answer to this crossword clue is the 7 letter word DOO-WOP
I've seen this crossword clue in The Guardian
D
O
O
-
W
O
P
Buddy explains!
The straight part
We know that "close harmony of the 1950s" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case close harmony of the 1950s = doo-wop.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 DOO-WOP mean?
DOO-WOP noun- A style of vocal-based rhythm and blues music popular in the mid-1950s to the early 1960s in America characterized by nonsensical backing vocals.