I look forward to hear from you.
I look forward to hearing from you.
Look forward to something means to feel happy or excited about something that is going to happen.
Use look forward to + noun/-ing: ‘I’m looking forward to the weekend.’ ‘I’m looking forward to seeing you.’
Here, to is a preposition, so use the -ing form after it, not the infinitive: ‘hearing’, not ‘hear’.
Check our grammar lesson on gerunds and infinitives.