Pompous nonsense suppressed by institute, not the first (7)
I believe the answer is:
orotund
'pompous' is the definition.
(thesaurus)
'nonsense suppressed by institute not the first' is the wordplay.
'nonsense' becomes 'rot' (I've seen this before).
'suppressed by' is an insertion indicator (I've seen this in other clues).
'institute' becomes 'found' ('found' can be a synonym of 'institute').
'not the first' means to remove the first letter.
'found' with its initial letter taken off is 'ound'.
'rot' going within 'ound' is 'OROTUND'.
(Other definitions for orotund that I've seen before include "Pompous - grandiose" , "Of speech, pompous and imposing" , "booming" , "Full, clear and musical" , "Resonant" .)