After walking—or rather riding—up the staircase to the Headmaster’s office, one knocks on the door, enters, and is greeted not only by the face of the Headmaster, or Headmistress, but by soft snores coming from the wall. We are first introduced to the Headmaster’s office, and the decorations it contains, in Chamber of Secrets (CS12). Here, the portraits are seen only sleeping, it is not until Order of the Phoenix that the portraits of the Headmasters begin to serve a purpose and to reveal themselves as important. However, I am getting ahead of myself.
First, a note on the title: assuming Albus Dumbledore had an average tenure as Hogwarts Headmaster, over 1000 years, Hogwarts would have had some where between 20 and 25 Headmasters and Headmistresses. That is, of course, unless Dumbledore had an exceptionally long tenure, then there would have been many more Headmasters. For the sake of argument, I am going to assume the number was around 20.
The portraits of the former Heads share many of the same qualities that other portraits in the Wizarding World have, in that they can travel to other portraits of themselves (unlike paintings of fictional people), they can converse with one another and living persons, and they are rather limited in their speech (EBF). However, being portraits of former Headmasters has gained them a unique quality. The portraits are duty-bound to serve the current (accepted) Headmaster or Headmistress (OP22). This provides a very interesting plot device. With this duty, the portraits must respect the instructions of the Headmaster, so that they may answer questions, offer advice, or travel to other locations as lookout. This brings us, naturally, to Harry Potter.
With the death of Albus Dumbledore, Harry is now mostly alone in his hunt for the Horcruxes, although Ron, Hermione, and possibly Ginny may help. While through his experiences Harry has become wise beyond his years, he is still only just of age and will undoubtedly need assistance in his search. Judging by Dumbledore’s actions and McGonagall’s questions at the end of Harry Potter and the Half-Blood Prince (HBP29), the other members of the Order of the Phoenix must not be entirely aware of the Horcruxes, or Dumbledore would have had at least some of the help. This leaves Harry to consult his only remaining source of information on Horcruxes: the portrait of Albus Dumbledore.
One imagines, as happened at the end of Half-Blood Prince, that Professor McGonagall will retain her spot as Headmistress. As a member of the Order, her position would be very beneficial to Harry. Even if Harry does not return to Hogwarts for formal schooling, Harry will undoubtedly need to go there, as it is probably the most powerfully magical place in wizarding Britain, if not the world. If allowed entrance to the Headmistress’s office, Harry would be left to question, with the instruction of McGonagall, the portraits of the former Heads, who, amongst themselves, possess one thousand years worth of historical and magical knowledge. Dumbledore, while limited to “catchphrases” (EBF), should still be able to offer some advice to Harry, if not instruction on the proper use of the Pensieve. As Dumbledore seems to be rather knowledgeable in the subject of creature relations (see, for example, his advice to Hagrid on how to treat the giants in OP20) he may be of some assistance in convincing other beings to join the Order’s cause. However, Dumbledore should not be the only Headmaster who could be of assistance in Harry’s quest. Armando Dippet, Dumbledore’s predecessor, may perhaps be of help in furthering Harry’s knowledge of young Tom Riddle’s mindset. Other Headmasters may also have portraits in other wizarding locations, less prominent than the Ministry or St. Mungo’s, but still helpful.
In conclusion, Harry Potter has quite a large task in front of him, though finally, for the first time in nearly 30 years, someone is on the right track to vanquish the Dark Lord. Along the way, Harry will need a lot of assistance, but he is certainly not alone in that. With the instruction of Dumbledore’s Army, Harry unknowingly developed himself something of an army, possessing a lot of knowledge necessary to their task. Spell power is not all that is necessary in a battle of this sort; one also needs a good amount of knowledge and wisdom. While members of the Order of the Phoenix will be of assistance, the 1000 years of knowledge tucked unnoticeably away at Hogwarts Castle is certainly not something to be ignored.