Dash over to look at Kirov's latest dancer (7)
I believe the answer is:
nureyev
'dancer' is the definition.
(Rudolf Nureyev)
'dash over to look at kirov's latest' is the wordplay.
'dash' becomes 'run' (I've seen this before**).
'over' says the letters should be written in reverse.
'to look at' becomes 'eye' (I've seen this before).
'latest' suggests the final letters.
The last letter of 'kirov' is 'v'.
'run' back-to-front is 'nur'.
'nur'+'eye'+'v'='NUREYEV'
(Other definitions for nureyev that I've seen before include "Rudolf -, Russian ballet dancer" , "Russian-born ballet dancer, who partnered Fonteyn, d. 1993" , "Rudolf -------, (1938-93), dancer" , "Fonteyn's dancing partner Rudolf" , "Rudolf -, Russ. dancer" .)