There's a difference between your FORM GAUGE and your DRIVE GAUGE
Your DRIVE Gauge shows how high your Drive can go, which is used for both Summoning and going into a Drive Form
When you go into a Drive Form, then your FORM GAUGE appears, which is a gauge that shows how long you can stay in that Drive Form
And when you Summon, your SUMMON GAUGE show up, and it does the same thing the FROM GAUGE does, only for Summons
The more you level up your Summons and Drive Forms, thier respective gauge's go up, until they max out at 9
The only way to level up your Drive Gauge is to continue on in the story, until eventually you get 6 after beating Saix, and 7 after defeating Sephiroth. The Drive Gauge can go no higher than 7 without using cheats
Edit: Meh, in the time time it took to type this, 3 people already said it <_<