Make things better for one politician getting over problems (7)
I believe the answer is:
improve
'make things better' is the definition.
(to improve something is to make it better)
'one politician getting over problems' is the wordplay.
'one' becomes 'i' (Roman numeral).
'politician' becomes 'MP' (Member of Parliament).
'getting over' says to put letters next to each other (in a down clue, some letters go above others).
'problems' becomes 'rove' (I can't explain this - if you can you should give a lot more credence to this answer).
'i'+'mp'+'rove'='IMPROVE'
'for' acts as a link.
Can you help me to learn more?
(Other definitions for improve that I've seen before include "Polish" , "Make better in quality" , "Ameliorate" , "Become better" , "pick up" .)