You’ve done the hard parts – Had your photo taken and chosen one you can live with. Congratulations!
But don’t rest on your laurels quite yet. If you don’t finish off the job correctly, you’ll have wasted much of your effort.
LinkedIn makes it very easy to upload your photo with clear instructions but you still have a lot of control about what appears. LI shows the view of what will appear according to how you crop it. Move it around until you get the best position.
I recommend a very tight crop – just your head and neck, maybe a little of your shoulders. It may depend on your hairstyle or the particular neckline of your jacket or shirt.
If the original photo has been taken with too little background, you’ll find you either need to use such a tight crop that part of your head is cut off or you’ll have white borders on the left and right. Some of the reasons I don’t recommend these white borders are:
It may not fill the full space – making it look like you didn’t know how to upload it correctly to LinkedIn, spoiling slightly an otherwise lovely photo.
It the background is dark it will show up even more.
It also cuts off the smaller photo snippet LinkedIn uses for other purposes: 
It may show a shadow at the top where the photo is:
So – remember to tell your photographer to give you enough background to work with in a crop so you don’t need to use white borders.
Make sure it fills the whole space. LinkedIn changed to a larger area for you photo a couple of years ago and some people’s photos stayed at the smaller size. You may be able to re-load the same photo if you still have it and it’s not too old. Otherwise, it’s time for a new photo!
Crop it close – I want to be able to recognize you when I meet you – not the tree in your backyard.
Please don’t have other people in your photo – not your wife or your kids. Make sure there aren’t any random “parts” of people (a hand on your shoulder or someone else’s hair) showing.
Do use a full face photo – not sitting at your desk or on the boat. There may be exceptions for some people in creative or professional fields where showing their “uniform” 
might be appropriate. If you go this route, do so thoughtfully and get a couple of opinions first. Otherwise, save these shots for your website or brochure.
Bottom line – a photo should be a true representation of you (on a good day) that will help me recognize you when we meet or know that I’ve got the right profile when I look you up after we’ve met.