Somewhat sooner (6)
I believe the answer is:
rather
I believe this is a double definition.
'somewhat' is the first definition.
(rather can mean somewhat or considerably)
'sooner' is the second definition.
('I'd sooner do this' means 'I'd rather do this')
(Other definitions for rather that I've seen before include "Prefer" , "On the contrary; more precisely" , "Fairly" , "with more justification" , "somewhat > sooner? > Quite" .)