In the last month in college, apply to do lots together (9)
I believe the answer is:
multitask
'do lots together' is the definition.
(to multitask is to do lots of things at once)
'in the last month in college apply' is the wordplay.
'in the last month' becomes 'ult' (letter-writing abbreviation meaning last month).
'in' is an insertion indicator.
'college' becomes 'MIT' (Massachusetts Institute of Technology).
'apply' becomes 'ask'.
'ult' inserted into 'mit' is 'multit'.
'multit'+'ask'='MULTITASK'
'to' acts as a link.
(Other definitions for multitask that I've seen before include "Do things simultaneously" , "execute jobs simultaneously" , "To perform several jobs" .)