Fourth in order took first place, backed by cheers (5)
I believe the answer is:
delta
'fourth in order' is the definition.
(fourth letter of the Greek alphabet)
'took first place backed by cheers' is the wordplay.
'took first place' becomes 'led' (as in taking the lead in a race).
'backed' says the letters should be written in reverse.
'by' is a charade indicator (letters next to each other).
'cheers' becomes 'ta' (both can informally mean thank you).
'led' back-to-front is 'del'.
'del'+'ta'='DELTA'
(Other definitions for delta that I've seen before include "Triangular patch of land at mouth of river" , "Alluvial river mouth" , "Area of distributaries in a river basin" , "Nile river mouth" , "Greek character" .)