Do you do any other exercise to strengthen your legs and core muscle?
Like squat, lunge, plank...etc. even do it with your own body weight, it will help. Also try do increase your run time or shorten your walk time bit by bit. You will see improvement.

You did the right thing. We need a longer time to develop a strong leg muscle and tendon. Be patient..remember to rest well so you body will develop and repair it self to be stronger. I'd say 4 months is too early to go hard on your leg..just increase your mileage with run walk.

While our cardiovascular adapt faster.

get a dog....
... to chase you at that 1km mark LOL

Kidding a side.

You have been running for 4 months so your muscles will be tone unless you still have sores or injury.
If sore or injury then healing and resting takes precedence.

In good shape, here is a tip to run continuously for 10km.
For me, I have to go back to finish up my laundry so i keep going.
You have to find your dog to motivate yourself.

Here is a technique.

What you can do is in your first 1 km, once you are running at your natural pace,
Pace your run:
Slower when you want to... or maybe for 30 seconds.
Faster when you want to... or maybe for 30 seconds.
Natural pace.... for 30 seconds.
Repeat in cycles.

Once you can pace yourself, when you feel like stopping but have 6km to go then...
slow the pace where your body can catch the breath you need.
Then return to your normal pace.

When you begin to feel tired or need to slow down, then slow down your pace.
When you slow down, let it happen naturally so you use less energy.
If you slow your pace deliberately and still using more energy then keep practising until you can slow down naturally.

When you are tired in your final km, think of your bladder.
You should be able to run to the lavatory faster to finish.

Hope these tips work for you and remember to get a dog, have fun.

When you slow down, let it happen naturally so you use less energy.
If you slow your pace deliberately and still using more energy then keep practising until you can slow down naturally.

I have a new suggestion for your consideration.
Heart is a muscle. The most important muscle.
Have you train your heart to keep fueling you at running speed to a distance of 7km non-stop?

2 or 3 more months of running you can finish a marathon but getting better at it take longer time.

Here an example how you can increase your mileage with run walk method if your leg not strong enough yet

As you mention your current fitness is
Run 1 KM walk and able to cover 6-7 KM

now,
Run 2 KM walk 30 sec for 6-7 KM

2 weeks later
Run 2 KM walk 30 sec for 8 KM

2 weeks later
Run 3 KM walk/stop to drink 30 sec for 8 KM

2 weeks later
Run 3 KM walk/stop to drink 30 sec for 10 KM

2 weeks later
Run 5 KM walk/stop to drink 1 min for 10 KM

. . .

Run 5 KM walk/stop to drink 30 sec for 15 KM (at this fitness level you should be able to do HM long run).

Go by feel. If it getting easier for you, there is no need to wait 2 weeks you can always interplay with the interval and total distance