Responsibility to catch one fish (6)
I believe the answer is:
plaice
'fish' is the definition.
(plaice is a kind of fish)
'responsibility to catch one' is the wordplay.
'responsibility' becomes 'place' (place can mean someone's responsibility or job).
'to catch' indicates putting letters inside.
'one' becomes 'i' (Roman numeral).
'place' going around 'i' is 'PLAICE'.
(Other definitions for plaice that I've seen before include "Important food fish" , "Ice, pal, will catch this fish" , "Flat fare" , "Large flatfish" , "Edible flatfish" .)