Proposes to suggest father's the puzzle! (4,3,8)

'proposes' is the definition.
('pop the question' can be a synonym of 'propose')

'father's the puzzle' is the wordplay.
'father's' becomes 'pop's' (pop is a kind of father).
'puzzle' becomes 'question' (I can't justify this - if you can you should give a lot more credence to this answer).
'pops'+'the'+'question'='POPS THE QUESTION'

'to suggest' is the link.
This may not be correct. Some or all of it may be part of another bit of the clue.

Can you help me to learn more?