A great big embrace at the end of the race (4)
I believe the answer is:
huge
'a great' is the definition.
(I've seen this before)
'big embrace at the end of the race' is the wordplay.
'big embrace' becomes 'hug' (I've seen this in another clue).
'at' says to put letters next to each other.
'the end of the' suggests the final letters.
The final letter of 'race' is 'e'.
'hug'+'e'='HUGE'
(Other definitions for huge that I've seen before include "Enormous" , "Mammoth" , "Jumbo" , "Vast; immense" , "giant" .)