Demanding old man follows his heart (7)
I believe the answer is:
exigent
'demanding' is the definition.
(similar in meaning)
'old man follows his heart' is the wordplay.
'old' becomes 'ex' (prefix meaning former or onetime).
'man' becomes 'gent' (gent is a kind of man).
'follows' means one lot of letters go next to another.
'heart' means to look at the middle letters.
The centre of 'his' is 'i'.
'gent' after 'i' is 'igent'.
'ex'+'igent'='EXIGENT'
(Other definitions for exigent that I've seen before include "Demanding immediate attention" , "Urgent and taxing" , "Pressing and urgent" , "Pressing; demanding" , "Urgent and exacting" .)