Leading institute beginning to consider subject (5)
I believe the answer is:
topic
'subject' is the definition.
(as in a topic for discussion)
'leading institute beginning to consider' is the wordplay.
'leading' becomes 'top' (both can mean first-class).
'institute' becomes 'i' (common abbreviation as in MIT).
'beginning to' suggests taking the first letters.
The initial letter of 'consider' is 'c'.
'top'+'i'+'c'='TOPIC'
(Other definitions for topic that I've seen before include "Matter for an argument" , "Theme of discourse" , "A subject for conversation or debate" , "Subject (for conversation, etc)" , "Issue (for discussion)" .)