Breathing device provided by popular, healthy king (7)
I believe the answer is:
inhaler
'breathing device' is the definition.
(pump used to aid breathing)
'by popular healthy king' is the wordplay.
'by' says to put letters next to each other.
'popular' becomes 'in'.
'healthy' becomes 'hale' (similar in meaning).
'king' becomes 'r' (r is abbreviation for rex).
'in'+'hale' is 'inhale'.
'inhale'+'r'='INHALER'
'provided' acts as a link.
(Other definitions for inhaler that I've seen before include "item of medical equipment" , "Spraying device to aid breathing" , "It helps asthmatic" , "Uninhibited smoker" , "Breather" .)