The most common and most likely answer to this crossword clue is the 6 plus 6 letter word MAIDEN SPEECH
M
A
I
D
E
N
S
P
E
E
C
H
More clues leading to the result MAIDEN SPEECH
Buddy explains!
The straight part
We know that "debut at Lords" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case debut at lords = maiden speech.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.