Popular coach, when heart deficient, so essential (9)
I believe the answer is:
intrinsic
'essential' is the definition.
('intrinsic' is associated in meaning with 'essential')
I cannot understand how the remainder of the clue works.
(Other definitions for intrinsic that I've seen before include "native?" , "Belonging by its very nature" , "Belonging as an inherent and essential part" , "Genuine" , "Natural" .)