My sister has sinus tachycardia while pregnant, will it go away after birth?

Possibly. Sinus tachycardia doesn't mean that there is an abnormality in your sisters heart rhythm. Sinus tachycardia is usually an appropriate rise in heart rate due to a real or perceived increased body need for oxygen, nutrients or temperature regulation. It is very common during pregnancy to become a bit anemic and this might easily explain the finding; she should see her doctor to make sure.
Yes. Sinus tachycardia is common in pregnancy. It should go away after delivery and if it doesn't, she should be evaluated.