Arctic swimmer raced north with Prince Harry (7)
I believe the answer is:
narwhal
'arctic swimmer' is the definition.
(type of whale found in the Arctic)
'raced north with prince harry' is the wordplay.
'raced' becomes 'ran' (running is a kind of racing).
'north' says the letters should be written in reverse (in a down clue, letters go up or 'northward').
'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 "Cetacean with large tusk" , "Warn Hal there's a whale here" , "Arctic toothed whale" , "Small tusked whale" , "Tusked sea mammal" .)