Old queen involved in cat fight the next day (8)
I believe the answer is:
tomorrow
'the next day' is the definition.
(I've seen this before)
'old queen involved in cat fight' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'queen' becomes 'r' (r is abbreviation regina. e.g. in ER ).
'involved in' means one lot of letters goes inside another.
'cat' becomes 'tom' (a tom is a male cat).
'fight' becomes 'row'.
'o'+'r'='or'
'tom'+'row'='tomrow'
'or' going within 'tomrow' is 'TOMORROW'.
(Other definitions for tomorrow that I've seen before include "___ Never Knows, 1966 Beatles song" , "It's manana in Spain" , "when weekend begins?" , "In 24-hours time" , "In the near future" .)