Systematic health check though half-hearted (10)
I believe the answer is:
methodical
'systematic' is the definition.
(similar in meaning)
'health check though half-hearted' is the wordplay.
I cannot really understand how this works, but
'though' could be 'tho' (synonyms) and 'tho' is present in the answer.
'health check' could be 'medical' (synonyms) and 'medical' is located in the remaining letters.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for methodical that I've seen before include "Orderly" , "following a set pattern" , "Systematic" .)