Herb Alpert's debut, one regularly covered by British Sign Language (5)
I believe the answer is:
basil
'herb' is the definition.
(basil is a kind of herb)
'regularly covered by british sign language' is the wordplay.
'regularly' becomes 'i' (I am not sure about this - if you are sure you should believe this answer much more).
'covered by' is an insertion indicator.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'sign language' becomes 'asl' (ASL is an example).
'b'+'asl'='basl'
'i' going into 'basl' is 'BASIL'.
'alpert's debut one' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
(Other definitions for basil that I've seen before include "Plant; Brush; Fawlty" , "Man" , "Saint" , "Name of male" , "Aromatic plant used as a herb" .)