If you are looking to compete in submission grappling then one of the main factors to consider and improve is fitness. This, in and of itself, is a vast subject.
Now, when I first began to compete, my supplementary training was primarily weight training and long slow distance running. In terms of strength development I scoffed at anything else other than weight training.
However when sparring with friends and training partners, while initially strong, I soon found myself running out of steam. Eventually, I had to admit, my physical training (while providing aesthetic benefits) was not functional for the goals I had.
When I fought in competition in the earlier days I relied too much on strength and this led to technically superior fighters often using this against me. Essentially, due to my supplementary training, I was gifting fighter