Offer new term for others going to American university, but not American (7)
I believe the answer is:
restyle
'offer new term' is the definition.
The definition suggests a verb in its base form which matches the answer.
'others going to american university but not american' is the wordplay.
'others' becomes 'rest' (eg the rest of a group).
'going to' is a charade indicator (letters next to each other).
'american university' becomes 'yale' (I've seen this before).
'but not' is a deletion indicator.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'yale' with 'a' taken out is 'yle'.
'rest'+'yle'='RESTYLE'
'for' acts as a link.
Can you help me to learn more?
(Other definitions for restyle that I've seen before include "Of hair, shape in different fashion" , "Fashion anew" , "Remake in a new form" , "Model afresh" , "new design" .)