There are lots of looking forward to questions, such as this one.
Can this sentence:
"I am looking forward to hearing from your reply"
Also be written as:
"I am looking forward to your reply"
Here are various options you can use (informal):
The following use 'I look' and are more formal versions of the above examples:
Note that 'hearing' can refer to written/read communication (letter, email or text). However, I avoid using 'hearing' to refer to emails. So when I submit a job application, I write 'I look forward to any communication from you ...'.
1. Credit to @user3724662, which is a very good answer.