Post the serial number of the tractor if you want detailed information on it. There were numerous changes in the design of the 997H in this era.
I'm presuming it has levers for steering, and it's not pedal steer. The steering clutches and brakes on the 977H are oil-immersed and the steering is operated by hydraulic boosters which are provided with oil pressure from the transmission pump.
When you pull a steering lever, it actuates a hydraulic spool which sends pressurised oil to a clutch piston adjacent to the steering clutches (on the inner side of the clutches).
The piston is sealed by a teflon/nylon piston ring and the oil pressure acting on the piston pushes it inwards to disengage the clutch.
The braking mechanism is straight mechanical, with a scissor-style actuation increasing the pedal pressure on the band to provide adequate braking force.
If oil is leaking out of the final drive, you need to determine exactly where this oil is leaking from.
Oil can only leak out of the final drive in basically two places - from the sprocket metal-to-metal type seal (where it appears as an oil leak around the sprocket hub) or between the FD case and the tractors main rear housing.
Leaks in either of these places is unrelated to steering clutch problems, and any FD leaks require FD disassembly.
The oil level in the steering clutch compartments is considerably higher than the FD's. There is a metal-to-metal face type seal on the FD pinion that prevents the steering clutch oil and FD oil from mixing.
The steering clutches utilise the transmission oil for lube and cooling, but the FD's have their own supply of gear oil, which should be a much heavier grade of EP gear oil.
If you're lucky, there may be a simple problem in the steering clutch hydraulic system. This is where you would start. The steering clutch booster spool valves may not be opening correctly due to worn or damaged or badly adjusted linkages.
The steering clutch spool valves may be contaminated with dirt, rust or water, making them not operate correctly. There are small pistons and tiny orifices in the spool valves and these all need to be spotlessly clean, and in good condition to operate correctly.
If the transmission filter changes have been neglected, the filter may have become overloaded with debris, and because the filter is a bypass type, it will dump debris back into the transmission oil when the filter is blocked, and this will then find its way into the steering clutch spool valves.
If the steering clutch hydraulics are just fine for adjustment, cleanliness and correct operation, then the problem is the steering clutch piston seal is gone - and this involves major surgery, by way of complete steering clutch removal.
Often, these piston seals chew out when the bevel gear cross-shaft bearings have started to collapse, and this then allows the cross-shaft to drop, which chews out the teflon/nylon piston seal.
If there's no equipment attached to the rear of the tractor, you can access the bevel gear compartment by taking off the plate on the vertical face of the rear of the housing, and then by placing a crowbar under the cross-shaft or even just against the bevel gear, and wriggling it, you can determine if the bevel gear bearings are O.K. or if they need replacement. There should be zero movement here.