Mariji S

I am taking pictures of the dog sport agility and at competitions it is hard sometimes to get close enough to the ring whilst dogs are competing. I have a Fujifilm finepix S5800 that has 10x optical zoom but am looking at buying a lens attachment for more zoom but also keeping the quality of my pictures as high as possible. I am a novice photographer and have only just learnt how to set up my cameras with the right ISO, aperture etc for these types of fast paced shots but unfortunately don't know anything about lenses. So would a telephoto or zoom lens be better for these types of pictures. Any information would help. Thank-You