Tweet from Papa -- "Extreme pressure besieging base" (4)
I believe the answer is:
peep
'tweet' is the definition.
(thesaurus)
'papa extreme pressure besieging base' is the wordplay.
'papa' becomes 'P' (NATO / phonetic alphabet).
'extreme pressure' becomes 'EP' (engineering term).
'besieging' is an insertion indicator.
'base' becomes 'e' (mathematical symbol).
'ep' enclosing 'e' is 'eep'.
'p'+'eep'='PEEP'
'from' acts as a link.
(Other definitions for peep that I've seen before include "Take quick look" , "Sly look (palindrome)" , "Look furtively (in both directions)" , "Look quickly" , "Secret look" .)