Due to the exterior of the TARDIS shrinking in ‘Flatline’ the Doctor spends much of the adventure trapped in his time machine. It is Clara who takes his role, out in the field, waving the sonic screwdriver around and taking charge.
The surprise is that this works really well, allowing the 12th Doctor to concentrate on solving the mystery. It has been well established by this point that not only is this Doctor not very good at dealing with people he doesn’t seem to enjoy it.
He, or a Time Lord with a similar temperament, might make this a permanent arrangement. Now we know that any TARDIS can be shrunk and made light enough to be carried there is no reason for companions to ever be without him.
If the Time Lord was happy within their TARDIS they could spend their downtime between adventures pottering away. When adventure calls the companion can simply carry the TARDIS in their bag, allowing tools and gadgets to be passed to them through the doors.
This might also be a good way to get around the problem of a Time Lord who is not physically capable, either due to age or injury. They could still help save the world from the comfort of their bed.
The Time Lord might have no choice about being in a shrunk TARDIS. This could be due to a technical failure or a form of punishment. This could be part of an on-going plot thread, with the Time Lord working to free themselves.
A shrunken TARDIS could change its exterior to make it easier to transport. This could be handbag or briefcase but it might be even smaller. It could be disguised as a wrist watch, pen or lucky charm. Something that wouldn’t arose suspicion if the companion carried it around for extended periods.
The concern would be that someone might take the TARDIS or it could be lost, which is what happens in ‘Flatline’. The difference being that as long as it had enough power the Time Lord could simply pilot the TARDIS back to the companion.
During the episode the Doctor ‘hacks’ Clara’s eyes so he can see what she sees (without her consent). We can only hope that he severs the connection or he’d be able to spy on her at any time. An ear piece allows them to communicate, completing the connection
It is possible that a Time Lord might have multiple companions or agents linked to their TARDIS. This would allow him to see and hear what is happening in multiple places while coordinating their efforts from the TARDIS control room.
This group of companions could span the universe or be placed throughout time, only activated with the Time Lord is in their vicinity and needs their help. This setup might be akin to the comic ‘Global Frequency’ (and many of ‘Global Frequency’ stories would fit Doctor Who).
Hooking up a companion in such a manner might also be a good safety precaution. Companions have a tendency to get captured or lost. It prove very useful for a Time Lord to find out where they are and give them guidance, no matter their circumstances.
A particularly mysterious Time Lord might recruit people without their knowledge. He could install his cameras and ear piece while the unwitting companion slept only to awake with an unknown voice telling them how to help those around them.
Identifying the owner of the voice and where and what their TARDIS is could be an ongoing mystery for the PCs to solve. Dare they ignore the strangers warnings when his information turns out to be correct?
If the Time Lord prefers more direct contact it is possible that they could arrange for their exterior doors to open up around head level. It could take the form of a box that opens to reveal their disembodied head, recalling Dorium’s fate in ‘The Wedding of River Song’. A more alien Time Lord might not understand why this disturbs others and embarrasses their companion.
The Doctor can provide instruction but he still needs Clara to do a lot for him. This puts a further emphasis on the companion, making them far more important to the story. They aren’t just following the Time Lord around, they are vital to the investigation.
Companions can take the initiative, ignoring the Time Lord in their ear to do what they think should be done. This could cause tension, especially if things don’t turn out as planned.
While the companion is doing the physical stuff and interacting with the locals the Time Lord can concentrate on deciphering the mystery. They could use the TARDIS memory banks to research the situation, analyse samples in the TARDIS labs or spend time building a gadget to defeat the monsters.
It would be important to ensure that they had plenty to do, even if they aren’t in the thick of the action. The sheer amount of resources available in their time machine might make things much easier for their companions as they’d always have the information they needed or the right tool to hand.
Time Lords who prefer to take the lead in physical action could establish the reverse of this situation. They might keep their companions within the safety of a portable TARDIS, leaving it to them to do research and spend time in the labs, safe from the terrors of the universe. Such a Time Lord might assemble a crack team of experts for any field, making up for his own lack of intelligence.
Once the situation has been resolved the TARDIS could either grow larger enough to whisk the companions to their next adventure or the Time Lord could retreat back into their solitary existence, awaiting for the next disaster.
PCs could encounter another Time Lord who has this arrangement. It could be that since the Time War he has shielded his presence by remaining in his own TARDIS. Now he might have a phobia about leaving the safety of its confines.
A sinister villain might collect miniature TARDIS and their trapped Time Lords. They could be a collector or they might treasure the knowledge the Time Lords can bestow. The villain might be posing as a hero, only for the PCs to learn the true source of his world saving skills. They could run the risk of joining the collection.