Sing country mostly having covered RB (6)
I believe the answer is:
warble
'sing' is the definition.
(I know that warble is a more specific form of the action sing)
'country mostly having covered rb' is the wordplay.
'country' becomes 'wales' (country of the UK).
'mostly' means to remove the last letter (most but not all of the word).
'having covered' indicates putting letters inside.
'wales' with its final letter taken away is 'wale'.
'wale' placed around 'rb' is 'WARBLE'.
(Other definitions for warble that I've seen before include "Sing with trilling sound, like bird" , "Sing like a thrush" , "Sing with gentle trilling note like some birds" , "Trill, yodel" , "Sing with trilling note - like bawler" .)