Puts on coat perhaps and disappears crossing river (9)

'puts on coat perhaps' is the definition.

'disappears crossing river' is the wordplay.
I cannot really understand how this works, but
'river' could be 'r' (abbreviation for river) and 'r' is found within the answer.
'disappears' could be 'vanishes' (vanishing is a kind of disappearing) and 'vanishes' is found in the remaining letters.
This accounts for all the letters.
This may be the basis of clue (or it may be nonsense).

'and' acts as a link.

Can you help me to learn more?