Clue: Princess turns up with model — backup model, female, carrying some fat (7,6)
Answer: ADIPOSE TISSUE
Explanation: Definition: carrying some fat
A charade of ADI, a reversal ('turns up', in a down light) of IDA ('Princess', comic opera by Gilbert and Sullivan) plus POSE ('model') plud TIS, a reversal ('backup') of SIT ('model') plu SUE ('female').The 'princess' is not DI, and neither 'model' is T.