Palace play badly after City up support (8)
I believe the answer is:
alhambra
'palace' is the definition.
(I've seen this before)
'after city up support' is the wordplay.
'after' becomes 'mah' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'city' becomes 'LA' (Los Angeles).
'up' is a reversal indicator (in down clue: letters go upwards).
'support' becomes 'bra' (a support for the breasts).
'mah'+'la'='mahla'
'mahla' reversed gives 'alham'.
'alham'+'bra'='ALHAMBRA'
'play badly' is the link.
This may not be right. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for alhambra that I've seen before include "Great 14th century Moorish palace near Granada in Spain" , "Famous Moorish palace near Granada in Spain" .)