It can take time to come back to a normal sleep routine and a good quality of sleep. Alcohol fucks up with the whole metabolism which of course includes severe fuck up of all physical conditions concerning sleep.
There are several good methods to support adaption to a normal sleep routine:
vitamin supplement to fill up the empty depots of literally everything, especially vitamin B complexes, vitamin D, C and mineral nutrients
stick to your schedule. going to bed every day at the same time creates stability.
meditate. meditation in general and before going to bed helps to calm the mind and lowers the resting heart rate.
Work on your sleep hygiene: no late coffee, go off all screens 1 h before sleep, only a light meal for dinner, no exercise 2 h before sleep, create a calm environment and deliberately put yourself to rest. Do something that comforts you, write a daily gratitude list, take a walk around the block every day (yes, every day), find out what helps you to end the day in a calm, structured way.
journalling helps to identify helpful and distracting patterns
if you constantly suffer from poor sleep please contact a doctor.
I disagree with this opinion. Not drinking alcohol does not obligatory lead to better sleep.
During the first weeks to months off alcohol people can experience phases with poor sleep, problems to fall asleep and waking up during the night as well as fatigue and the need for more hours of sleep. That is pretty normal.
Sleep should improve/adapt to normal within the first year of recovery. Constant sleeplessness or chronic poor sleep should undergo medical diagnosis.
Absolutely. Just skied out west for a few days and this was the first time I’ve ever done a ski trip without drinking in the evenings. Such a better experience because I was getting quality sleep, waking up refreshed and was alert all day. Sleep is good, booze is bad
My sleep is so much better since being alcohol free for 130 days.
My whole life routine is on track better than it had been over past 2 yrs.
But i im awake from as early as 4am but mostly up at 5am every morning. If i go to sleep too early (9pm)then im up at 1-2am struggling to fall back asleep.
I thought it may have something to do with my previous unhealthy diet and lack of exercise, so i eat healthy most days now and also aim to get my 10,000 steps in a day and sometimes more if i have time to try to wear myself out. But since quitting alcohol i cant sleep past 5am - im not complaining though i always used to struggle rising early and now i get to start the day nice and early which then helps my mental health too.
Be patient 
It will improve. Your body just needs a bit more recovery time. The B12 complex and vit D are great ideas and they helped me a lot.