Those people start to engage in subject (5)
I believe the answer is:
theme
'subject' is the definition.
('theme' can be a synonym of 'subject')
'those people start to engage' is the wordplay.
'those people' becomes 'them' (I've seen this before).
'start to' indicates taking the first letters.
The first letter of 'engage' is 'e'.
'them'+'e'='THEME'
'in' is the link.
(Other definitions for theme that I've seen before include "issue" , "Motif or melody" , "Musical motif" , "Short melody" , "argument" .)