Crossword Genius

Relaxed having lowered pulse (8)

Ross

I believe the answer is:

downbeat

'relaxed' is the definition.
(I've seen this before)

'lowered pulse' is the wordplay.
'lowered' becomes 'down' (similar in meaning).
'pulse' becomes 'beat' (synonyms).
'down'+'beat'='DOWNBEAT'

'having' acts as a link.

(Other definitions for downbeat that I've seen before include "Casual" , "Low-key" , "Dismal and depressing" , "Gloomy; laid-back" , "Miserable; relaxed" .)

I've seen this clue in The Times and The Sun.
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