Extremely educated geek occasionally gets head start (4)
I believe the answer is:
edge
'head start' is the definition.
(I've seen this in another clue)
'extremely educated geek occasionally' is the wordplay.
'extremely' means to remove the middle letters (only the extremes of the word are used).
'occasionally' means one should take alternating letters (letters taken at regular intervals or occasions).
'educated' with its middle taken out is 'ed'.
The alternating letters of 'geek' are 'ge'.
'ed'+'ge'='EDGE'
'gets' is the link.
(Other definitions for edge that I've seen before include "Sharp ridge" , "Sharpened side of blade" , "Border or cutting side of knife" , "Advantage (informal)" , "incisiveness" .)