The most common and most likely answer to this crossword clue is the 5 letter word ONCER
O
N
C
E
R
Buddy explains!

The straight part
We know that "evensong enough for me" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case evensong enough for me = oncer.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 ONCER mean?
ONCER noun- A one-pound note.
- A person who does something once.
- A single sexual encounter between two individuals, a one-night stand.
- A person with whom one shares a single sexual encounter, a one-night stand.