Fish swimming ashore starts to seem exhausted (3,5)
I believe the answer is:
sea horse
'fish' is the definition.
(sea horse is a kind of fish)
'swimming ashore starts to seem exhausted' is the wordplay.
'swimming' indicates an anagram.
'starts to' says to take the initial letters.
The initial letters of 'seem exhausted' is 'se'.
'ashore' with letters rearranged gives 'seahor'.
'seahor'+'se'='SEA-HORSE'
(Other definitions for sea horse that I've seen before include "Small fish with equine-like head." , "Graceful swimmer" , "Upright swimmer" , "Small upright fish with equine head" , "Small fish swimming upright" .)