Apart from that would you be artifically increasing her wages over and above what she would normally be paid just so that she can return some of it to you as rent? As Bronte mentions an au pair will probably be considered part of the family for the duration of the stay and as far as I know things like rent a room relief and private rental accommodation now have rules requiring transactions to be "at arm's length" and not between, say, family members in most or all cases. You should certainly get authoritative, professional advice if you are not sure before attempting to claim this relief. Sounds unlikely that you will be able to to me.