First person put on quiet network (4)
I believe the answer is:
mesh
'network' is the definition.
('mesh' can be a synonym of 'network')
'first person put on quiet' is the wordplay.
'first person' becomes 'me' (first-person pronoun**).
'put on' says to put letters next to each other.
'quiet' becomes 'sh'.
'me'+'sh'='MESH'
(Other definitions for mesh that I've seen before include "Web" , "Engagement" , "Interconnected configuration" , "Net, snare" , "Grid, netting" .)