Placement of flyers plugging trendy joint (10)
I believe the answer is:
'placement' is the definition.
(internship is a type of placement or work position)
'flyers plugging trendy joint' is the wordplay.
'flyers' becomes 'terns' (tern is a type of bird).
'plugging' is an insertion indicator (I've seen this in other clues).
'trendy' becomes 'in' ('in' can mean fashionable).
'joint' becomes 'hip' (part of body).
'terns' placed inside 'inhip' is 'INTERNSHIP'.
'of' is the link.
(Other definitions for internship that I've seen before include "practical training programme" , "being a trainee?" , "Work experience position" , "Trainee's spell" .)