A miser and his favourite fish? (10)
I believe the answer is:
cheapskate
'a miser' is the definition.
(cheapskate is a kind of miser)
'his favourite fish?' is the wordplay.
'his favourite' becomes 'cheap' (I can't justify this - if you can you should give a lot more credence to this answer).
'fish?' becomes 'skate' (skate is a kind of fish).
'cheap'+'skate'='CHEAPSKATE'
'and' acts as a link.
Can you help me to learn more?
(Other definitions for cheapskate that I've seen before include "Scrooge" , "One's tight" , "ungenerous person" , "Miserly type" , "Tightwad" .)