My dear sister can be translated to 우리 사랑하는 언니.
This means My 언니 that I love.
우리 means actually 'our' but Korean people use 우리 as "my" sometimes as well like my house 우리 집, my country 우리 나라, my mom 우리 엄마.
In Korea, we don't really use 'dear'.
If you are writing a letter, you usually just say "우리 언니에게"
which means 'to my sister'. Or you can say
사랑하는 우리 언니에게 'to sister that I love'
I miss you. 언니가 보고싶어요.
When you miss someone, casually you can use 보고싶어요.
In Korea, 'You' is '너'. But we only call someone 너 who are same age as you or younger than you. If she's older than you, you say "언니 보고싶어요.", if she's younger than you, you can say "너가 보고싶어"
You can just say "보고싶어" or "보고싶어요" because Korean people omit subjects a lot.
I'd say 사랑하는 우리 언니, 보고싶어요.
I hope it will help you (: