Posh set contains odd characters seeking attention (4)
I believe the answer is:
'seeking attention' is the definition.
(sound made to get someone's attention)
'posh set contains odd characters' is the wordplay.
'contains odd characters' means one should take alternating letters (only the letters in odd-numbered positions).
The alternating letters of 'poshset' are 'PSST'.
(Other definitions for psst that I've seen before include "Sibilant interjection to call attention" , "Attention-seeking noise" , "way of attracting attention" , "Sound of call to hear a secret" , "Notice me" .)