Cerebral and popular, order European, punctual, to dismiss pun (12)
I believe the answer is:
intellectual
'cerebral' is the definition.
(I know that cerebral can be written as intellectual)
'popular order european punctual to dismiss pun' is the wordplay.
'popular' becomes 'in' ('in' can mean trendy).
'order' becomes 'tell' (as in ordering or telling someone to do something).
'european' becomes 'E' (abbreviation e.g. EU).
'to dismiss' indicates named letters should be taken away.
'punctual' with 'pun' taken out is 'ctual'.
'in'+'tell'+'e'+'ctual'='INTELLECTUAL'
'and' acts as a link.
(Other definitions for intellectual that I've seen before include "Highly-developed thinker" , "Brainy person" , "Person with a highly-developed mind" , "Scholarly" , "Egghead" .)