The most common and most likely answer to this crossword clue is the 7 letter word SOLFEGE
S
O
L
F
E
G
E
Buddy explains!
The straight part
We know that "An exercise in singing" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case an exercise in singing = solfege.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 SOLFEGE mean?
SOLFEGE noun- A method of sight singing that uses the syllables do (originally ut), re, mi, fa, sol (or so), la, and si (or ti) to represent the seven principal pitches of the scale, most commonly the major scale. The fixed-do system uses do for C, and the moveable-do system uses do for whatever key the melody uses (thus B is do if the piece is in the key of B). The relative natural minor of a scale may be represented by beginning at la.