Tate played Donna Noble, who had to stop being the Doctor's companion after the final episode of the rebooted fourth series due absorbing the "power of the Time Lords".
Tennant as the 10th Doctor, who he played between 2005 and 2010, had to wipe her mind to save her life during the 2008 episode.
David Tennant (here in the title role alongside Kylie Minogue) will revisit Doctor Who. (AP PHOTO)
Tennant regenerated as the 14th Doctor during the first female Time Lord Jodie Whittaker's last episode in 2022, signalling his return for three 60th anniversary episodes.
During a new episode on Saturday, Heartstopper star Yasmin Finney stars as Donna's daughter, Rose, and she meets Tennant as the Doctor along with her mother.
Donna does not recognise the Doctor and fails to pay attention when a UFO is seen in the sky.
The Doctor then gets a lift from Donna's husband Karl Collins, with actor Shaun Temple reprising the role, who explains she gave away her lottery winnings.
Jacqueline King also comes back as Sylvia Noble, who has concerns about Donna's state of mind.
Rose meets a fluffy alien called the Meep, voiced by Harry Potter star Miriam Margolyes, and when Donna is upset by the discovery, the Doctor returns to see her at home.
The Doctor wants to know about Wilfred "Wilf" Mott, previously played by the late actor Bernard Cribbins - who died last year aged 93, and she says "he's not with us anymore".
The Doctor replies: "I loved that man, I'm so sorry for your loss" before they explain that Wilfred is in sheltered accommodation.
Donna, the Doctor and her family are then captured and put in the back of a van.
Donna and the Doctor escape and she follows him into the Tardis where she says she does not mind "dying" to save her daughter.
The Doctor then returns her memories in an emotional moment before it is revealed that the Time Lord being genderfluid means Donna and Rose can share the knowledge she has and will not be in danger.
A new larger Tardis is then revealed, which has a coffee machine, before it catches fire and the Doctor teases that might now "end up anywhere in time and space".
Saturday's The Star Beast is the first of three special episodes, marking the 60th anniversary.
It will be followed by Wild Blue Yonder on December 2 and The Giggle on December 9.
Both Tennant and Tate previously returned to the series.
Tate also appeared when a two-part special was broadcast over 2009's Christmas and 2010's New Year's Day.
During the 50th anniversary special, Tennant made a comeback during Matt Smith's tenure for The Day Of The Doctor in 2013.
Also returning for the new swathe of episodes is showrunner Russell T Davies.
Sex Education and Barbie star Ncuti Gatwa will then take over in the role of the Doctor over the festive period as he becomes the 15th Doctor.
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