I'm going to go against the grain here a little bit here...
You've got a new job. You had good reasons to leave the last place and go find a new job - whether it be topic, pay, conditions, lack of career progression opportunities, etc.
Your new job requires 100% of your attention while you're there. If they sense you are 'moon lighting' by keeping the old job going, they'll be annoyed and you'll be in trouble. Do you want this?
As you've already left your previous job, if the post matters to them, they'll be looking to hire someone to take over from where you left off.
If not, they'll be looking to get away from whatever projects you were keeping going before you left.
Either way, the amount of work your previous employer has for you to do is probably quite low and you will have to give up your evenings and weekends to work for them, so you are perfectly entitled to charge whatever you like for contract rates, but please bear in mind the following:
- Whatever you charge (say $180/hour), you have to deliver good value on this. You are not going get paid to read email or do on-line learning.
- Emails and phone calls to arrange, hand-over, clarify the work shouldn't really be billed, but use some common sense here.
- No expenses claims - how much is a phone call, really?