Medical problem damaged hearts without time to get suitable drug (10)
I believe the answer is:
heatstroke
'medical problem' is the definition.
(heatstroke is a medical complaint)
'damaged hearts without time to get suitable drug' is the wordplay.
I cannot really understand how this works, but
'hearts' could be 'h' (abbreviation used in card games e.g. bridge) and 'h' is present in the answer.
'time' could be 't' (abbreviation) and 't' is present in the answer.
'suitable' could be 'ok' and 'ok' is found within the answer.
'drug' could be 'e' (E is another name for ecstasy) and 'e' is found in the answer.
'to get' could be 're' (I've seen this in other clues) and 're' is located in the remaining letters.
This explanation may well be incorrect...
(Other definitions for heatstroke that I've seen before include "Complaint from Sun" , "Sickness" , "Kos at three (anag) - cause of high temperature?" , "Exhaustion from too much sun" , "It may incapacitate" .)