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Adi Shankaracharya aside from being a Vedantin scholar is also described by many to have been a Sri Vidya Upasaka. The Soundarya Lahari, a principle Sri Vidya text, is often attributed to Him.
In the Sri Vidya Sampradaya, there are three distinct Guru Paramparas namely Lopamudra, Hayagriva and Ananda Bhairava.
Which particular Guru Parampara does Adi Shankaracharya fall in?
I will be quoting from the Shri VidyA manual Nityotsava. I have a hard copy of the text.
The 3rd Chapter ( quoting from pp. 100-102) of the text (called as Shri Krama) has the relevant information.
Here, we get the Guru Paramparas related to the HAdi and KAdi schools of Shri VidyA. And, then we also find the Guru Parampara of an allied school called in the text as ManvAdi. Adi Shankara belonged to this particular Paramapara.
Any Guru Parampara will have the Divyaugha (the Divine line), Siddhaugha (the Rishi line) and the Manavaugha (the human line) Gurus.
The aspirant belonging to a particular Parampara is required to worship these higher Gurus before starting their daily rituals.
The Mantras given for the MAnavaugha Gurus for the ManvAdi school are only relevant for us and they are as follows:
MAnavaughah :
Aim Hrim Shrim Uttara-anandanAtha-ShripAdukAm pujayAmi tarpayAmi namaha ||
Parama-Anandanatha ..,
Sarva-jyAna-AnandanAtha ...,
Sarva-Anandanatha ,
Siddha-Anandanatha,
Govinda-anandanAtha,
Shanakara-AnanadanAtha-ShripAdukAm pujayAmi tarpayAmi namaha ||
From these Mantras we get the following line of human Gurus.
Uttara-Anandanatha> Parama-Anandanatha> SarvajyAna-Anandanatha> Sarva-Anandanatha> Siddha-AnandanAtha> Govinda-AnandanAtha> Shankara-AnandanAtha.
Among these Gurus, the last human Guru, ShanakarAnandanAtha, is identified as Adi Shankaracharya. And, Govindapada is also there in the list. The suffix "Ananda-NAtha" signifies the fact that all these aspirants belong to certain Shri VidyA SampradAya. During initiations they will be given such Anandanatha suffixed names by their Gurus.
Now, at the start of this section on the ManvAdi school, the author (i.e. Bhaskara RAya's disciple UmAnandanAtha) writes:
ManvAdi-vidyAnAm Guru-paramparA ||
atha sutra-kritAnuktA-nAmapi Shri-vidyAtmano-palakshitAnAm manvAdi-vidyAnAm Guru-paramparyam yathA -----
Even though the SutrakAra (i.e. Parashurama) did not mention (anything about this Parampara in his work-Kalpa Sutra), since it is considered as allied to Shri VidyA, the Guru Parampara of the ManvAdi-VidyA is also given here:
And, at the end of the section he writes:
Kalpasutrasya kali-matAntargatatvat idam pAram-parjya-trayam tadanugameva |
VidyArnava-ukta ShrishodashAkshari-guru-pAdukA-pAramparyasya kAdi-kAli-ubhaya-mata-sammatatvam jyeam ||Since Kalpasutra is included in the KAli school, these three aforementioned Paramparas are followers of it. It is to be noted that the Guru Parampara of the Shodakshari VidyA, as found in the VidyArnava Tantram, is in accordance with both the KAdi and the KAli schools.
Therefore, the answer is -- a Guru Parampara called ManvAdi, where the disciples are worshippers of the Shodashi Mantra of the Goddess.
