Arctic swimmer raced northward with Prince Harry (7)
I believe the answer is:
narwhal
'arctic swimmer' is the definition.
(type of whale found in the Arctic)
'raced northward with prince harry' is the wordplay.
'raced' becomes 'ran' (running is a kind of racing).
'northward' says the letters should be written in reverse (in down clue going up).
'with' becomes 'w' (abbreviation).
'prince harry' becomes 'Hal' (name for the young Henry V in Shakespeare's plays).
'ran' reversed gives 'nar'.
'nar'+'w'+'hal'='NARWHAL'
(Other definitions for narwhal that I've seen before include "Tusked sea mammal" , "Small Arctic whale" , "Tusked marine creature" , "Ocean mammal" , "swimmer" .)