Moderate exposed lie underpinning American university entrance (8)
I believe the answer is:
mitigate
'moderate' is the definition.
(I've seen this before)
'exposed lie underpinning american university entrance' is the wordplay.
'exposed' means to look at the middle letters (the inside of the word is exposed).
'underpinning' means one lot of letters go next to another (in a down clue, some letters go under others).
'american university' becomes 'mit' (Massachusetts Institute of Technology).
'entrance' becomes 'gate' (type of entrance).
The central letter of 'lie' is 'i'.
'i' after 'mit' is 'miti'.
'miti'+'gate'='MITIGATE'
(Other definitions for mitigate that I've seen before include "Lessen - modify" , "Extenuate" , "Reduce the severity of, say a sentence" , "Appease" , "Assemble" .)