Keep going to make an offer of? (4,3)
I believe the answer is:
hold out
'keep' is the definition.
(thesaurus)
'going to make an offer of?' is the wordplay.
'going to' means one lot of letters go next to another.
'make' becomes 'hold' ('hold' can be a synonym of 'make').
'an offer of?' becomes 'out' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'hold' next to 'out' is 'HOLD OUT'.
Can you help me to learn more?
(Other definitions for hold out that I've seen before include "Resist (against siege)" , "Offer as inducement or resist capture" , "Offer - last" , "Offer inducement or maintain resistance" , "Resist difficulties" .)