Social climber at college wants to get going (7)
I believe the answer is:
upstart
'social climber' is the definition.
(thesaurus)
'at college wants to get going' is the wordplay.
'at college' becomes 'up'.
'wants' means one lot of letters go next to another.
'to get going' becomes 'start' ('start' can be a synonym of 'get going'**).
'up'+'start'='UPSTART'
(Other definitions for upstart that I've seen before include "Unexpectedly fresh" , "Presumptuous and arrogant type" , "Bold newcomer" , "Nouveau-riche" , "Social climber or wise guy" .)