Rather sore, perhaps, on entering (6)
I believe the answer is:
sooner
'rather' is the definition.
('I'd sooner do that' means 'I'd rather do that')
'sore perhaps on entering' is the wordplay.
'perhaps' indicates an anagram.
'entering' means one lot of letters goes inside another.
'sore' is an anagram of 'soer'.
'soer' going around 'on' is 'SOONER'.
(Other definitions for sooner that I've seen before include "nickname of US State" , "Rather" , "At an earlier time" , "Earlier or preferably" , "native of Oklahoma" .)