A second city's somersaulting dance (5)
I believe the answer is:
salsa
'dance' is the definition.
(type of dance)
'a second city's somersaulting' is the wordplay.
'second' becomes 's' (common abbreviation).
'city's' becomes 'LA's' (Los Angeles).
'somersaulting' says the letters should be written backwards (letters flip or somersault over).
'a'+'s'+'las'='aslas'
'aslas' written backwards gives 'SALSA'.
(Other definitions for salsa that I've seen before include "Steps" , "Latin American dance - spicy Mexican sauce" , "Hot dance - hot sauce" , "This could be hot" , "Tomato relish" .)