improve (to become better): Your English will improve with practice.
get better informal (to improve): Don’t worry; things will get better soon.
look up informal (to get better): At last, things are starting to look up for us. My financial situation is looking up.
pick up (to increase or get better): The economy is starting to pick up again. The sales usually pick up in the spring.
perk up (to increase or get better): House prices are likely to perk up.
take a turn for the better (start to get better): I’m sure the situation will take a turn for the better.