To make a 1:7 gearing you would need to have two gears where the one being driven has 7 times the number of teeth relative to the driving gear. The only lego technic combination that has this ratio is an 8 tooth gear driving a 56 tooth turntable, however a turntable is not that suited to a gearing system as it has no center. The next option is to create a gear train that produces an overall 1:7 gearing ratio. There are many ways of doing this and the general technique is to create a ratio with a 7 as the denominator and then to cancel out the numerator with a matching reciprocal gearing ratio. For example 2 / 7 could be followed by 1 / 2 to make 2 / 7 x 1 / 2 = 1 / 7. Similarly 3 / 7 could be followed by 1 / 3 to make 3 / 7 x 1 / 3 = 1 / 7. There are more combinations that follow this pattern.

The first option is shown below. Here a 2 / 7 is created by driving a 28 tooth gear with an 8 tooth gear and then the 1 / 2 is created in the gear train with a 12 tooth driving a 24 tooth gear to create an overall 1:7 gearing ratio between the yellow and brown axles.

This is quite a compact solution and gives a close axle spacing between the axles (2 lego units).

If you need a greater distance between the axles you could use the 3 / 7 x 1 / 3 technique. Here 3 / 7 is made by driving a 28 tooth gear with a 12 tooth gear - now these can't be connected directly on a whole number regular grid so an intermediate 20 tooth gear is used to connect them. Finally the 1:7 gearing ratio is created by adding a 1 / 3 gearing ratio at the beginning of the gear train (an 8 tooth driving a 24 tooth gear) to give the overall solution below:

Here the overall gearing ratio between the yellow and dark blueish axle is 1:7 and has a spacing of 7 lego units. The topology of the gears can be changed to create many more possible lay outs.