Parrot perhaps – when sick? (5-4)

'sick?' is the definition.
I know nothing about this answer so I can't tell whether this works.

'parrot perhaps' is the wordplay.
I cannot quite see how this works, but
'parrot perhaps' could be 'bird' (parrot is a kind of bird) and 'bird' is located in the answer.
The remaining letters 'dicky' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

'when' acts as a link.

Can you help me to learn more?