Raise favourite son to get degree (4)
I believe the answer is:
step
'degree' is the definition.
(thesaurus)
'raise favourite son' is the wordplay.
'raise' shows that the letters should be reversed in order.
'favourite' becomes 'pet' ('pet' can be a synonym of 'favourite').
'son' becomes 's'.
'pet'+'s'='pets'
'pets' backwards is 'STEP'.
'to get' is the link.
(Other definitions for step that I've seen before include "Abrupt change; pace" , "Manner of walking" , "bit of a dance" , "A pace for pets" , "Football" .)