Keep going, having disposed of energy guzzling appliance (7,2)
I believe the answer is:
soldier on
'keep going' is the definition.
(I've seen this before)
'disposed of energy guzzling appliance' is the wordplay.
'disposed of' becomes 'sold' (dispose of can mean to sell something).
'energy' becomes 'e' (physics symbol as in E=mc2).
'guzzling' means one lot of letters goes inside another.
'appliance' becomes 'iron' (iron is a type of appliance).
'e' put into 'iron' is 'ieron'.
'sold'+'ieron'='SOLDIER ON'
'having' acts as a link.
(Other definitions for soldier on that I've seen before include "Don't give up" , "... to bear up" , "Persist in spite of difficulties" , "keep going" , "Keep struggling" .)