The most common and most likely answer to this crossword clue is the 7 letter word RHYTHMS
I've seen this crossword clue in The Guardian
R
H
Y
T
H
M
S
Buddy explains!
The straight part
We know that "Beats/Beats/the longest possible unchanging word/the longest possible unchanging word" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case beats/beats/the longest possible unchanging word/the longest possible unchanging word = rhythms.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 RHYTHMS mean?
RHYTHMS noun- The variation of strong and weak elements (such as duration, accent) of sounds, notably in speech or music, over time; a beat or meter.
- A specifically defined pattern of such variation.
- A flow, repetition or regularity.
- The tempo or speed of a beat, song or repetitive event.
- The musical instruments which provide rhythm (mainly; not or less melody) in a musical ensemble.
- A regular quantitative change in a variable (notably natural) process.
- Controlled repetition of a phrase, incident or other element as a stylistic figure in literature and other narrative arts; the effect it creates.