Bit of a hand to cover second song (5)
I believe the answer is:
psalm
'song' is the definition.
(I've seen this before)
'bit of a hand to cover second' is the wordplay.
'bit of a hand' becomes 'palm' ('palm' is part of 'hand').
'to cover' means one lot of letters goes inside another.
'second' becomes 's' (common abbreviation).
'palm' going around 's' is 'PSALM'.
(Other definitions for psalm that I've seen before include "Sacred poem (written by King David?)" , "Palms (anag.)" , "Church hymn" , "Lamps (anag) -- song" , "OT hymn" .)