Slayer's debut record had an election catchphrase (6)
I believe the answer is:
slogan
'catchphrase' is the definition.
(eg a political catchphrase)
'slayer's debut record had an' is the wordplay.
'debut' suggests taking the first letters.
'record' becomes 'log' (log is a kind of record).
'had' says to put letters next to each other.
The initial letter of 'slayers' is 's'.
's'+'log'+'an'='SLOGAN'
'election' is the link.
This may not be right. It may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for slogan that I've seen before include "Logo" , "War cry - advertising jingle" , "Word or phrase adopted as motto" , "Memorable advertising phrase" , "short political statement" .)