Record label millions love, tenor's first to admit (6)
I believe the answer is:
motown
'record label' is the definition.
(Motown is an American record label)
'millions love tenor's first to admit' is the wordplay.
'millions' becomes 'm' (abbreviation).
'love' becomes 'o' (love means zero in tennis).
'tenor's first' becomes 't' (1st letter of 'tenor').
'to admit' becomes 'own' (own can mean to admit or acknowledge).
'm'+'o'+'t'+'own'='MOTOWN'
(Other definitions for motown that I've seen before include "Detroit and American record company" , "Tom won (anag) - music" , "form of music" , "Detroit musical style" , "Genre of music originally from Detroit" .)