Swim right into the awful claw (5)
I believe the answer is:
crawl
'swim' is the definition.
(crawling is a kind of swimming)
'right into the awful claw' is the wordplay.
'right' becomes 'r' (common abbreviation).
'into' indicates putting letters inside.
'the awful' is an anagram indicator.
'claw' with letters rearranged gives 'cawl'.
'r' going into 'cawl' is 'CRAWL'.
(Other definitions for crawl that I've seen before include "be overrun" , "Way of swimming" , "inch" , "Grovel" , "Go slow" .)