Cat’s important role, secondarily in economy (5,4)
I believe the answer is:
maine coon
'role secondarily in economy' is the definition.
I know nothing about this answer so I cannot judge whether this works.
'cat's important' is the wordplay.
I cannot really see how this works, but
'important' could be 'main' (similar in meaning) and 'main' is located in the answer.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for maine coon that I've seen before include "Very large breed of cat" , "Unusually big cat" .)