The first one was Michael Goodliffe, who appeared briefly in The Man With The Golden Gun.
Wow, I don't remember this at all
...where was he? I must be getting old...
According to the Wikipedia article
, he's in M's office at the beginning of the film, when they show Bond the letter and the gold bullet with "007" engraved on it. He's never identified by name in the scene.
Come to think of it, I don't think he's identified by name in For Your Eyes Only
either; Frederick Gray (the Minister of Defence) and Tanner are in M's office (standing in for the deceased Bernard Lee), but Bond only greets them as "Minister... Chief of Staff." It's not until GoldenEye
that we see Bond and Tanner as friends (though I can't remember if that was established in Fleming, or not until the Gardner novels when Tanner became a regular supporting character).
In response to the OP, my favorite Tanner would have to be Michael Kitchen, since he's the only one so far to even have a semblance of a character.