Much to alter, perhaps, in a heartless guy (7)
I believe the answer is:
greatly
'much' is the definition.
(I've seen this before)
'alter perhaps in a heartless guy' is the wordplay.
'perhaps' indicates an anagram.
'in' means one lot of letters goes inside another.
'a heartless' says to hollow out the word (remove centre letters).
'guy' with its centre taken out is 'gy'.
'alter' with letters rearranged gives 'reatl'.
'reatl' placed inside 'gy' is 'GREATLY'.
'to' is the link.
(Other definitions for greatly that I've seen before include "To a large extent" , "Very much" , "to a considerable extent" .)