What line of action do you expect Afghan Taliban to take againt TTP?
a) Go hard against TTP and ensure they are not able to operate against Pakistan.
b) Use TTP as a leverage against Pakistan. Give and take policy to extract maximum concessions from Pakistan
c) Down the line, join TTP as their ideological brethern to implement their version of Sharia across the border.
Its simple,
Taliban will keep their word on Afghanistan not being used against any neighbouring country. Not to mention they are already at war with TTP Mohmand group. They dont support BLA and never have.
If you dont take their word for it, consider it their necessicity. Pakistan recognition of their governemnt is very important for them. It is Pakistan who is acting as a bridge between them and China aswell. With the fallout with the west after their military takeover they need Pakistan, China, Russia comes with defacto support of central asian countries, Iran. War for them will be over, now they need to rule and the more content the population is the more stable their governemnt will be.
Have you noticed one more very important player is also onboard, Iran, had it deployed Fatemiyon or supported hazara shite warlords ( they never resisted Taliban either)
The fall of the north without fighting through backchannels, Hikmatyar, Massood, Atta, Rabbani are all on board. Balk just went down without fighting as soon as ANDSF commander surrendered, Atta never resisted just played to the gallery. Now jamat is coming to Pakistan tomorrow including Rabbani and i think Masood aswell.
This was much more than a military takeover, it was done at multiple levels also involving bordering countries.
Pakistan has been very clear from the start and at the top levels the Taliban also fully understand the importance and potential for regional connectivity.
Basically Pakistan has to take care of the problem within its border now (TTP/ISKP, BLA and PTM).
First few months or a year will be rough, than it be peaceful.