Yes, every time you level up your stats will go up to according to which class you are. Starting at level 5 you gain the ability to train your strength and accuracy and at level 9 you'll be able to train mentality and stamina.
To train one of your skills you'll need to spend a training point which you'll get at level 5 and each level after. Click on your management icon or hit H and then got to the training section and choose what you wish to train.
Be careful because if you raise only one skill and ignore the others your golf game will suffer. Putting all points into power will make each shot cost more and more stamina while also causing the swing bar to speed up. If you put all your points into accuracy each shot will cost more and more mentality and you will lack the power to make the longer shots required to reach par in the higher leveled courses.