Former pupil with new steer promises to be unpleasant (9)
I believe the answer is:
obnoxious
'be unpleasant' is the definition.
(synonyms)
'former pupil with new steer promises' is the wordplay.
'former pupil' becomes 'OB' (abbreviation for 'Old Boy' - private school pupil).
'with' says to put letters next to each other.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'steer' becomes 'ox' (a steer is a castrated ox).
'promises' becomes 'IOUs' (promises to pay a debt).
'ob'+'n'+'ox'+'ious'='OBNOXIOUS'
'to' acts as a link.
(Other definitions for obnoxious that I've seen before include "Thoroughly offensive and objectionable" , "Foul" , "Nasty" , "Repugnant" , "Extremely unpleasant" .)