Lion-headed monster to correspond with hawk-headed god (7)
I believe the answer is:
chimera
'lion-headed monster' is the definition.
(I've seen this before)
'with hawk-headed god' is the wordplay.
'with' means one lot of letters go next to another.
'hawk-headed' becomes 'chime' (I can't justify this - if you can you should give a lot more credence to this answer).
'god' becomes 'ra' (Ra is an example).
'chime' next to 'ra' is 'CHIMERA'.
'to correspond' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for chimera that I've seen before include "Vain, foolish, or incongruous fancy" , "Wild creation of mind, or monster of Greek myth" , "Illusory achievement; mythical beast" , "figment of the imagination" , "Each rim (anag) - foolish fancy" .)