They go out in pursuit when leader's gone missing by river (6)
I believe the answer is:
exeunt
'they go out' is the definition.
(stage direction meaning 'they exit')
'pursuit when leader's gone missing by river' is the wordplay.
'pursuit' becomes 'hunt' (synonyms).
'when leader's gone missing' means to remove the first letter.
'by' is a charade indicator (letters next to each other).
'river' becomes 'exe' (River Exe).
'hunt' with its initial letter taken off is 'unt'.
'unt' put after 'exe' is 'EXEUNT'.
'in' is the link.
(Other definitions for exeunt that I've seen before include "Stage direction to a group of actors (Latin)" , "(Actors) leave stage" , "direction to get cast away" , "They leave (stage direction)" , "More than one exit?" .)