Set one's sights higher and improves (5,2)
I believe the answer is:
looks up
'set one's sights' is the definition.
Although both the answer and definition are verbs in their -s form, I don't see how they can define each other.
'higher and improves' is the wordplay.
'higher' becomes 'up'.
'and' means one lot of letters go next to another.
'improves' becomes 'looks' (I can't explain this - if you can you should give a lot more credence to this answer).
'up' put after 'looks' is 'LOOKS UP'.
Can you help me to learn more?
(Another definition for looks up that I've seen is " Seeks in reference book - takes eyes off book".)