Remain after others leave relative to cross river (4,2)
I believe the answer is:
stay on
'remain' is the definition.
('stay on' can be a synonym of 'remain')
'relative to cross river' is the wordplay.
'relative' becomes 'son' (son is a kind of relative).
'to cross' is an insertion indicator.
'river' becomes 'tay' (Scottish river).
'son' placed around 'tay' is 'STAY ON'.
'after others leave' acts as a link.
This may not be right. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for stay on that I've seen before include "Remain after normal time" , "stick" , "Remain after others have left" , "Remain behind" .)