At this point, it seems that there will be a need for memos and meetings detailing changes in the level of adherence to SOP. Advise people that there will be plenty of memos/meetings, but that they will decrease as time goes by.
Also, brand any troublemakers with a hot iron.
You may also want to make sure that work is distributed appropriately. Sometimes the people who tend to get things done get the lion’s share of the work simply because they’ll actually do it. Others need to be held accountable as well.
And as mentioned above, many people probably won’t be happy about the change in management, but you’re not there to make friends. Definitely be understanding and sympathetic, but that doesn’t mean be a doormat. Lots of bosses can’t tell the difference. I had to have a “talking to” with an employee this week after an escalation. It was the first time I’d had to do that.
This person is usually very clear-headed, but she was pulling a “not my job.” Technically, she was right, but we had a federal deadline to meet and the work that wasn’t her job was pretty easy. Regardless, she knew she wouldn’t be able to convince someone else to do it before the deadline, but she refused to do it herself and our largest client would’ve been pissed. They don’t care who’s responsible for doing the work internally. Anyway, she had been my friend before I was made the boss and I can tell you it was the hardest thing I’ve done since I’ve worked at this company.
Any place where I’ve worked, your “job” is to do what the people paying you ask you to do so that the project/team/department/company can be successful.
Usually it’s just easier to resolve a morale problem by getting rid of the people with low morale.
It all depends on the type of company you work for. Innovative, high performance companies tend to look for people who want to be there and want to succeed. Bureaucratic, officious companies tend to hire drones who only want to do their specific drone job so they can collect a paycheck. The former tends to do everything possible to either help someone succeed if they can and want to, or get rid of them quickly if they can’t. In the other sort, forget about implementing any change because the system won’t let you. Better off just going to your office and locking the door so your underdrones can’t bother you.
And some managers distribute the work to the people they like best, even though those people do not get it done. Others distribute the work along the lines of “whomever is at hand when something comes up, gets it”: in one of my lab jobs, the guy with the degree in admin was in charge of work requiring stats, while one with training in process control had been assigned our supplies; switching them made both of them happier and the two tasks run better!
And every secretary/admin. I had a director who introduced himself to the secretary first thing when visiting someone. He said it was the way he could always get his calls through. I took his advice. He moved to Denver to run our factory there. When I visited him for a meeting, the first thing I did was introduce myself to his secretary. Well, a blizzard was blowing up, and she told me that she got me a room at an airport hotel just in case. And that was the reason I spent the night in a nice bet and not on a bench at Stapledon.
Looking to be an auspicious beginning. On Monday I’ll be taking charge of 12 excepted employees in an office generally staffed by 63. I assume their office will be similar to my current one, with the excepted employees putting out fires as they arise and doing their best to handle currently scheduled matters - with no clear plan or ability to extend that schedule into the future, or to process all aspects of the current caseload.
Then at some time in the future, I’ll enjoy having a bunch of pissed off employees returning from layoff, thrilled at the prospect of working harder than usual to clear up the backlog.
Doing my best to keep a positive attitude. Just has required a bit of a shift in my mindset. For some time now I had been thinking about how I would best present myself to the office as a whole, who I would meet when, what I would prioritize… Has required me to shift my thinking a bit if I will only have 20% of my staff.
Oh well - at least it will be a lot cheaper for me to buy donuts for 12 on my 1st day than it would have been for 63! 
When I was a kid, I wanted to be “the boss”. Not a fireman or a vet or astronaut… I just wanted to be the guy in charge. Didn’t matter what I did as long as I was the one on top.
Sadly, I have nothing to tell you because my experiences have been in the private sector and I have no experience running things in a government office, where I feel the culture and the freedom to do what you want is rather… limited… from what I’m used to. 
Anyway, congratulations!