May purr, or turn up with a hiss (4)
I believe the answer is:
puss
'may purr' is the definition.
Although both the answer and definition are singular nouns, I cannot see how one could define the other.
'turn up with a hiss' is the wordplay.
'turn' says the letters should be written in reverse.
'with' says to put letters next to each other.
'a hiss' becomes 'ss' (I can't explain this - if you can you should give a lot more credence to this answer).
'up' back-to-front is 'pu'.
'pu'+'ss'='PUSS'
'or' is the link.
Can you help me to learn more?
(Other definitions for puss that I've seen before include "For example, a Persian" , "clock" , "It might be a tortoiseshell" , "Feline" , "Moggie" .)