The most common and most likely answer to this crossword clue is the 7 letter word RUDOLPH
I've seen this crossword clue in The Daily Telegraph
R
U
D
O
L
P
H
More clues leading to the result RUDOLPH
- Chap coming from game left public house after party
- Christmas present drawer acting as a guide
- 13, 18’s leading light
- Hurl pod out for one of Santa’s team?
- Leader of reindeer facing terrible hold-up?
- End of December hold-up involved a seasonal visitor
- Hold-up, unfortunately, behind start of race for reindeer
- Reindeer hold up roaming after mid-march
- After start of race, hold-up involved reindeer
Buddy explains!

The straight part
We know that "Leader of reindeer facing terrible hold-up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case leader of reindeer facing terrible hold-up = rudolph.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.