Let's begin with the TTP:
The TTP, or Tehrik-e-Taliban Pakistan, is a relatively new organization only being founded in 2007. The group is comprised of a number of smaller groups--twenty-eight to be exact--mainly located in the tribal areas of Pakistan as well as in Punjab (Movement of the Taliban in Punjab) and Baluchistan (Movement of the Taliban in Baluchistan). Despite being a little out-of-date, as several members listed here are now dead, this list of the TTP's top leaders does a great job showcasing the groups long history and ties with al-Qaeda.
Moreover, after the failed Times Square bombing by the TTP, the group was added to our list of designated terrorist organizations. In the same announcements, the State Department said this of the TTP and AQ: "The T.T.P. and Al Qaeda have a symbiotic relationship: T.T.P. draws ideological guidance from Al Qaeda, while Al Qaeda relies on the T.T.P. for safe haven in the Pashtun areas along the Afghan-Pakistani border...This mutual cooperation gives T.T.P. access to both Al Qaeda’s global terrorist network and the operational experience of its members. Given the proximity of the two groups and the nature of their relationship, T.T.P. is a force multiplier for Al Qaeda".
In May of 2012, the Long War Journal also reported on the documents released from the bin Laden raid. In some of these documents, there were communications between AQ and the TTP with the former asserting its authority over the latter. Being that the TTP continues to shelter AQ and there have been little to no reports of infighting, it appears the TTP listened to AQ.
The Haqqani Network, based in Afghanistan and the tribal areas of Pakistan is a Taliban subgroup.
The US State Department has designated various members of the HQN as terrorists, as well as blacklisting the entire group as terrorists in 2012. The US Treasury Department has also blacklisted various Haqqani militants, including Saidullah Jan, Yahya Haqqani, and Muhammad Omar Zadran. These three individuals have extensive roles within both the HQN and the Taliban; they also have deep connections to al-Qaeda (AQ).
According to the Treasury Department, Saidullah was not only designated for being a top leader in the Haqqani Network, but was also "was trusted by Al-Qaida (AQ) members as an HQN associate who could help with any trouble, including arrest". Yahya was noted as serving "as a liaison between the HQN and AQ and he has maintained ties with AQ since at least mid-2009. In this role, Yahya has provided money to AQ members in the region for their personal expenses. As of mid-2009, he acted as the HQN’s primary liaison with foreign fighters, including Arabs, Uzbeks, and Chechens". Finally, Zadran was " in charge of smuggling explosives into Afghanistan" for HQN and various militant groups.
These aren't the only members with extensive ties to AQ; Sirajuddin Haqqani, Jalaluddin Haqqani's son (Jalaluddin is the founder and spiritual leader of the Haqqani's), is thought to be a member of AQ's top Shura council; Khalil al-Rahman Haqqani, Jalaluddin's brother, is a key fundraiser for HQN and AQ and serves on behalf of AQ's shadow army, Lashkar al-Zil, in Afghanistan. (Read more: Here)
Lashkar-e-Jhangvi (LeJ) is a Pakistan-based terrorist organization that carries out attacks in both Pakistan and Afghanistan and committing sectarian killings within Pakistan. According to the Long War Journal, LeJ has "integrated themselves with al-Qaeda" and often "serves as muscle for al-Qaeda terror attacks". To further showcase the levels of interconnection between Pakistani jihadist groups and al-Qaeda, in 2010 a guy named Qari Zafar was killed in a US drone strike. Qari Zafar was a leader within both LeJ and another Pakistan-based group Fedayeen-e-Islam, which is an alliance of members from the TTP, LeJ, AQ and another group by the name of Jaysh-e-Mohammad.
Lashkar-e-Tayyba (LeT) is yet another terrorist organization based in Pakistan that has extensive ties to both the TTP and AQ. Throughout the years, LeT has ran numerous training camps for al-Qaeda and their network of a plethora of terror groups in Pakistan. Not only that, but Usama bin Laden and Abdullah Azzam were very instrumental in the persuasion of Hafiz Saeed to found the LeT. LeT fighters also took part in a deadly raid on a joint-US-Afghan outpost in Wanat, which left nine Americans dead and around fifteen Americans and Afghans wounded.
Islamic Movement of Uzbekistan:
The Islamic Movement of Uzbekistan (IMU) is a Pakistan-based group fighting for an Islamic state in Uzbekistan, but assist al-Qaeda and the TTP in operations in both Pakistan and Afghanistan (the most recent being the Karachi airport raid). According to the United Nations, the IMU was founded at the behest of al-Qaeda and Usama bin Laden with bin Laden supplying most of the funding for its creation. They also go on to say that several IMU leaders have also been top leaders within al-Qaeda.
The groups listed here do not form an exhaustive list; there are plenty more Pakistan-based groups with extensive ties to al-Qaeda (a good read on that). However, the groups listed show just how intertwined these groups and al-Qaeda are. After all, these groups (and so many more) form a syndicate with al-Qaeda where a "victory for one is a victory for all". One of these groups within the syndicate is the TTP. Knowing all this, it makes it seem unlikely that with how intertwined and close they are to AQ that they will switch sides and go to the Islamic State. Likewise, it seems unlikely for a slew of Pakistan-based groups to switch teams. But stranger things have happened.