It demands attention in extremely pompous way (4)
I believe the answer is:
psst
'it demands attention' is the definition.
(sound made to get someone's attention)
'extremely pompous way' is the wordplay.
'extremely' means to remove the middle letters.
'way' becomes 'st'.
'pompous' with its centre removed is 'ps'.
'ps'+'st'='PSST'
'in' acts as a link.
(Other definitions for psst that I've seen before include "Whispered exclamation to attract attention" , "attempt to make secret contact" , "Sibilant interjection to call attention" , "Pay attention" , "Sibilant sound made to attract attention" .)