Rush died beside tree (4)
I believe the answer is:
dash
'rush' is the definition.
(dashing is a kind of rushing)
'died beside tree' is the wordplay.
'died' becomes 'd' (abbreviation next to the year of someone's death).
'beside' is a charade indicator (letters next to each other) (I've seen this in other clues).
'tree' becomes 'ash' (ash is a kind of tree).
'd'+'ash'='DASH'
(Other definitions for dash that I've seen before include "Short line; run" , "Splash of colour" , "Morse code symbol" , "style" , "gratuity" .)