Relaxed having lowered pulse (8)
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" .)