This puzzle is part of the Puzzling StackExchange Advent Calendar 2021. The accepted answer to this question will be awarded a bounty worth 50 reputation.
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In the style of the author's Cryptic Family Reunion puzzles, this puzzle is a list of twelve thematically related words, each clued cryptically, with the theme to be determined. Since the definition part of a cryptic clue would give away the theme, these cryptic clues use one of Santa's reindeer (you know, Dasher and Dancer and Prancer and Vixen, Comet and Cupid and Donner and Blitzen...but do you recall, the most famous reindeer of all? ...Rudolph) to stand in for the definition part of the clue. In addition, if you put the clues in the correct order, you will find a gift which is the final answer to the puzzle. No partials, please. I hope you enjoy!
- Starting to pull during landing, Vixen? (5)
- Now, at last, relieved from flying around world with Comet (4)
- Rudolph left, leaving me with Prancer (4)
- Farinaceous breakfast excludes oat seed, saving a (bit of) tummyache for Vixen (9)
- Needle pointing north? Down Rudolph! (4)
- Edgily, Dasher set even closer to Dancer, keeping mum about Donner (7)
- Comet provided essential help to Cupid (4)
- After they threw down outside, Blitzen at an end with Donner (3)
- Initially, giving out oats, Santa excluded Rudolph (5)
- East-facing departure after delay positioning Dancer (4)
- Kringle holding on to Blitzen (4)
- New replacement for Prancer's leader in exchange for Dasher (4)