Initially warmed to that fellow for every snivel (7)
I believe the answer is:
whimper
'snivel' is the definition.
(I've seen this before)
'initially warmed to that fellow for every' is the wordplay.
'initially' indicates taking the first letters.
'to that fellow' becomes 'him' ('him' refers to a man).
'for every' becomes 'per' ('per' means 'for each' or 'for every').
The first letter of 'warmed' is 'w'.
'w'+'him'+'per'='WHIMPER'
(Other definitions for whimper that I've seen before include "Whine" , "Cry weakly or softly" , "Complaint" , "Sob" , "Cry feebly or plaintively" .)