Sings rhythm and blues primarily in part of UK (7)

'sings rhythm' is the definition.
(to warble is to sing)

'blues primarily in part of uk' is the wordplay.
'blues primarily' becomes 'rb' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'in' means one lot of letters goes inside another.
'part of uk' becomes 'Wales' ('Wales' is part of 'uk').
'rb' inserted inside 'wales' is 'WARBLES'.

'and' acts as a link.