The way I have improved my footage is a mixture of a control system like the posts above with things I have read about video techniques that are not specifically to do with aerial photography.
It depends on the style of the footage you want I suppose and that can be very personal and subjective but the most important thing I have learned which is applicable to filming both with my dSLR and Mavic Pro is to make everything as smooth as possible and in most cases that means 'Slow'. I am forced to use a fluid video head with my camera as it is far too heavy to hold still never mind pan slowly. This gives a lovely smooth result and I have tried to copy this on the Mavic.
At first the results from the Mavic were poor but after a lot of reading I learned that a lower shutter speed and frame rate looked better. Then I softened a lot of the movements the Mavic made. Specifically I made the gimbal work much more slowly and smoothly so instead of changes in pitch appearing jerky they became more fluid. Then I changed some of the aircraft control responses with the same aim in mind.
The next thing I did was to practice, practice, practice multi stick inputs eg increasing pitch to go forwards at the same time as applying yaw with the left stick to turn the head. Get the combination in the right proportion and you can fly smoothly in a circle. When you get good at that you can mix in some elevation changes. These can look good and in fact DJI has preprogrammed one of the more famous effects into one of the intelligent flight modes which is when you are filming a subject and the Mavic flies away backwards and climbs at the same time. This effect looks good and is used widely on amateur youtube videos. Even after I learned to be able to put the aircraft where I wanted it to be and keep things in view it is still very difficult to keep enough concentration to fly slowly and smoothly for very long and I relied on the editor a lot !
Before getting downhearted at so much to learn, the good news is that I next discovered Litchi which did everything for me ! I would now go so far as to say it is now essential to use the Waypoint functionality that the Litchi app gives me combined with their mission planning system. With this I have found that I can get better footage than I can take with manual control - even better than tripod mode which I suggest is your best option if using DJI Go4. In short, what it does is to move the gimbal smoothly during the flight and you can program in the route and any elevation changes and tell it what to look at as flies along. It can then switch views very smoothly by interpolating the angles between them. IMO it produces footage that looks smoother than when flying manually. The downside is you have to preplan everything but having a plan is also something I have learned is a really good idea.
Finally, all the above has taught me what I like. Last week I flew freehand and used some of the transitions that I had leaned looked good whilst practising using Litchi flying round my house. The results were a lot better than I used to get and meant less time editing the raw footage afterwards. I