Tiny heartless firm taking on magnate (6)
I believe the answer is:
tycoon
'magnate' is the definition.
(I know that magnate can be written as tycoon)
'tiny heartless firm taking' is the wordplay.
'heartless' suggests removing the centre.
'firm' becomes 'co' (a firm is a company).
'taking' becomes 'on' (eg one taking drugs is 'on' drugs).
'tiny' with its middle taken out is 'ty'.
'ty'+'co'+'on'='TYCOON'
'on' is the link.
(Other definitions for tycoon that I've seen before include "Rich and powerful businessman" , "Rich powerful person" , "Business magnate or mogul" , "top businessman" , "Powerful industrialist" .)