Since they changed her mechanics. I think that the jungle is the role where you can get the most out of her skills now.
The cougar on level one makes jungling easy and fast.

The key to jungle faster is obviously use both instances.
You need to keep changing and using all the skills whenever they are ready.

Level 1 : Start with Primal Surge hit , heal , Aspect Of The Cougar, Swipe Smite.

Level 3 and on :
Javelin Toss you can use this at a distance to start .
Place a Bushwhack
Go for Aspect Of The Cougar
Swipe
Pounce
Takedown

Primal Surge when necessary.
Smite when necessary .

Ganking is the strongest point here.
Since the synergy between human and cougar are stronger, you will want to keep this and mind and get the best out of it.

Position yourself in a place your target can't see you and try to hit a Javelin Toss
If you hit the spear , go for Aspect Of The Cougar and Pounce on your target , since the first jump have improved range . Swipe to reset the cooldown. Takedownfor damage, and that should be enough for your mate to finish your enemy.

If you miss the spear, you can try to go out of your position, place a Bushwhack under your target and do the cougar combo .

if you miss both your cougar combo will not be as strong , but you can still help your mate and try for a kill .

if everything fails just jungle a bit more and keep trying.